What would happen is we would desperately need many more wolves again.

Not at all.

Wolves don't need any help adjusting to an increase in their food supply. What you will end up with is, "What are we going to do about this wolf problem?" That's not a problem you want to have.

What you will more realistically end up with is an increase in auto insurance premiums in rural and outer suburban areas. Deer/vehicle collisions will become more common and they are expensive claims to pay.

I thought it would be obvious that I'm referring to the fact that prior to overpopulation of people, there developed a sustainable balance between wolves, elk, etc. We eliminated the wolves, and that is what led to the overpopulation of deer etc. So, the point is that we either fill the role of the wolves we eliminated or we bring back the wolves. The overpopulation of deer doesn't work.

I'm not sure about elk, but deer tend to have an alpha male that mates with multiple females, so shooting a buck doesn't damage the population as much. I think that's why antelope hunting is gender-agnostic and you need to win a lottery to do it: They're monogamous, so killing a male has the same impact on the population as killing a female.

It seems a lot more likely that killing males would discourage them from being monogamous than that killing males would have the same population impact as killing females.

If you assume that they adapt the way human cultures do to such influences, which isn't necessarily true of animal populations.

The only things you need to assume are that they're alive and their mode of reproduction is obligately sexual. As far as the prediction is concerned, humans are totally irrelevant.

Evolutionary pressure is a harsh mistress.

I am not sure how well Heinlein's polyandrous Loonies[1] would match real-life scenarios. This did not happen in New South Wales where male convicts outnumbered the female convicts six to one[2].

[1] https://en.m.wikipedia.org/wiki/The_Moon_Is_a_Harsh_Mistress [2] https://en.m.wikipedia.org/wiki/Convict_women_in_Australia

Males and females are not symmetrical. A female who never reproduces because she wants to be faithful to a mate who doesn't exist is giving up 100% of her reproduction. A female who stays faithful to a mate who does exist is giving up 0%, in terms of quantity -- one mate can provide all the children a female is capable of having.