The stuff you're saying is an outdated and largely discredited way of looking at mating - for animals and for humans. I seriously doubt there are many current peer reviewed sources to support it. I warn you, this is long - but if you want a scientifically supported explanation, that's what it's going to take:

First off, what you are saying about the female being the chooser and the male the pursuer is not always the case in the animal kingdom - not by a long shot.

"This helps to explain why, contrary to the historical understanding that promiscuity is generally the preserve of males, it’s now clear that female promiscuity is abundant across the animal kingdom—from fruitflies20 to humpback whales21—and is “widespread” among primates.22 This revelation owes a large debt to the DNA paternity-testing techniques that have enabled researchers to part the veils of discretion that previously obscured rampant female promiscuity (most particularly in many supposedly monogamous female birds).23 Consider the lek: a mating arrangement in which males compete with each other in a specific territory or arena in a winner-takes-all conflict for sexual access to females. It is the paradigm case of competitive males and choosy females. But in some species, on closer inspection with the benefit of paternity-testing techniques, it has been turned upside down.

For example, observations over two years of the buff-breasted sandpiper, a beautiful shore bird, suggested that in line with traditional expectations of how leks operate, one fortunate male was seen to be involved in 80 percent of matings in the first year, and 100 percent in the second.24 Well worth him taking any risk to reach that top-bird position, you would think. But DNA paternity testing of over 160 offspring hatched during that time revealed that much had taken place out of sight. Far from one or two males having all the reproductive luck, at least fifty-nine different males had fertilized eggs in the forty-seven broods tested! (Eggs from the same brood can have different fathers.) This meant that “there were actually more fathers than mothers.”25 Recall, there’s supposed to be only one father shared among the entire community of mothers. Moreover, most males only bore offspring with a single female, yet a remarkable 40 percent of the broods had more than one father.

Take the big cats, such as the lioness who might, during estrous, mate as many as a hundred times a day with multiple lions. Or, consider savanna baboons, reported to actively seek numerous, brief pairings.26 Yet somehow observations such as these failed to make much of a conceptual dent: perhaps because, as Hrdy wryly suggests, “theoretically the phenomenon should not have existed.”27 (As anthropologists like to quip: “I would not have seen it if I hadn’t believed it.”)28

In short, neither promiscuity nor competition are necessarily the preserve of male reproductive success. And a third challenge to the intuitive force of Bateman’s principles is that males can be choosy too. This, of course, makes no sense if you start from the assumption that, for them, mating comes at the rock-bottom price of a single sperm from a limitless supply. But this turns out to be a profoundly misleading way of thinking about the situation. Take, for instance, the presumed dizzying abundance and trivial cost of male sperm. As a number of scientists have pointed out, both observation and personal experience attest to the fact that males do not offer up a single sperm in exchange for an egg.37 They instead produce millions of sperm at a time (in humans, on the order of two hundred million)38 that luxuriate in the gland secretions that make up semen. While the situation varies from species to species, biologists have concluded that, in general, “the antiquated notion that males can produce virtually unlimited numbers of sperm at little cost is demonstrably incorrect.”

Given all the complications of the original Bateman story, it’s unsurprising that there turns out to be no straightforward relation between parental investment and parental care either. For many years, people were so carried away by the dizzying reproductive possibilities of males that they forgot to ask where all the females-to-be-fertilized were to come from.50 Overlooked was the fact that most of the females might already be busy with existing offspring. On average, male reproductive success can’t outstrip that of females, due to the simple fact that every offspring has both a father and a mother. As evolutionary biologists Hanna Kokko and Michael Jennions point out, the theoretical possibility that a male could produce dozens of offspring if he mated with dozens of females is of little consequence if, in reality, there are few females available to fertilize.

Whether or not paternal care evolves in a species seems to depend on the interaction of many different factors not yet fully understood. But certainly, it is much more common in birds and fish than in mammals, where gestation and lactation impose such huge biological start-up costs on the mother. Yet an exception to this are the primates, among some of which, at least, paternal care is common: “many males routinely protect, rescue, patrol, baby-sit, adopt, carry, shelter, feed, play with and groom infants.”

Then there's the issue of the actual practicality and chance of success with the "spreading his seed" theory:

As psychologist Dorothy Einon points out: “In the time taken for a woman to complete the menstrual cycle that releases one ovum, a man could ejaculate . . . 100 times”1 (although one hopes he wouldn’t be so childish as to actually count). It’s been estimated that, in what are described as “optimal” breeding conditions, a woman could bring about fifteen children into being in her lifetime.2

Consider, Einon posits, a woman who on average has sex once a week for thirty years. Now suppose she bears a generous brood of nine children. As you can easily calculate for yourself, on average she will have sex 173 times per child. And for each of the 172 coital acts that didn’t lead to a baby, there was a partner involved, having nonreproductive sex. To explore what this means for any man trying to reach the benchmark set by Schmitt of scoring a century of infants in a year, it’s worth following Einon in breaking things down to clearly see the schedule involved. First, the man has to find a fertile woman. For the benefit of younger readers, it may be worth pointing out that throughout most of human evolution the Tinder app was not available to facilitate this. Nor, as observed in the previous chapter, was there likely to have been a limitless supply of fertile female vessels for men to access. In historical and traditional societies, perhaps as many as 80–90 percent of women of reproductive age at any one time would be pregnant, or temporarily infertile because they were breast-feeding, Einon suggests. Of the remaining women, some of course would already be in a relationship, making sexual relations at the very least less probable and possibly more fraught with difficulties.

Let’s suppose, though, that our man manages to identify a suitable candidate from the limited supply. Next, he has to prevail in the intense competition created by all the other men who are also hoping for casual sex with a fertile woman, and successfully negotiate sex with her. Say that takes a day. In order to reach his target of one hundred women per annum, our man then has just two to three days to successfully repeat the exercise, ninety-nine more times, from an ever-decreasing pool of women. All this, mind you, while also maintaining the status and material resources he needs to remain competitive as a desirable sexual partner. So what’s the likely reproductive return on this exhausting investment? For healthy couples, the probability of a woman becoming pregnant from a single randomly timed act of intercourse is about 3 percent, ranging (depending on the time of the month), from a low of 0 to a high of nearly 9 percent.5 On average, then, a year of competitive courtship would result in only about three of the one hundred women becoming pregnant.6 (Although a man could increase his chances of conception by having sex with the same woman repeatedly, this would of course disrupt his very tight schedule.)7 This estimate, by the way, assumes that the man, in contradiction with the principle of “indiscriminately mating,” excludes women under twenty and over forty, who have a greater number of cycles in which no egg is released. It also doesn’t take into account that some women will be chronically infertile (Einon estimates about 8 percent), or that women who are mostly sexually abstinent have longer menstrual cycles and ovulate less frequently, making it less likely that a single coital act will result in pregnancy. We’re also kindly overlooking sperm depletion, and discreetly turning a blind eye to the possibility that another man’s sperm might reach the egg first. In these unrealistically ideal conditions, a man who sets himself the annual project of producing one hundred children from one hundred one-night stands has a chance of success of about 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000363.8

Among various hunter-gatherer societies, whose way of life is supposed to best reflect our ancestral past, the estimated maximum number of children a man can sire is twelve to sixteen: not so different from that of women (which is nine to twelve).

All quotes and science taken from:

Fine, Cordelia. Testosterone Rex: Myths of Sex, Science, and Society (p. 49). W. W. Norton & Company. Kindle Edition.

If this topic interests you, I highly recommend this author and this book in particular. Her research is extensive and meticulous.