These people are simply delusional. The very worst outcomes for children, particularly boys, are if they live in a contentious home where their parents fight all the time. Those are the ones most likely to become juvenile delinquents and substance abusers, not kids raised by single parents/moms.
In addition, no fault divorce also saves men's lives. If the only way you can get away from your abusive husband is to kill him, at least some women will do that. The rates of this also came down with the advent of no-fault divorce.
You are exactly right, fewer people will marry if this gets pushed through. It's just one of their many, many poorly thought out ideas.