There are some important differences between polygamy and its problems in religious sects as opposed to legalizing it in general. I am not arguing for or against legalization, but the differences matter.
(Before proceeding, let me apologize for using economic terms like “shortages” and “supply” with reference to women. Women are not a commodity, but since that is how religious polygamist sects tend to treat them, I hope you will bear with me as I use the terms here.)
Religious polygamist sects indeed do experience shortages of women. It has serious consequences, most of them not good. But the sects tend to be small, closed communities. It’s doubtful that people in society at large would enter into polygamy in sufficient numbers to cause a supply problem.
Religious polygamist sects, at least Mormon-based ones, make polygamy mandatory. A man with but one wife is not worthy of Heaven, and a woman who doesn’t accept sister wives will be “destroyed,” according to Mormon scripture. All of that, and the competition to be more righteous than the next guy by accruing more wives, accelerates the creation of shortages. By contrast, legalized polygamy will not be mandatory. I doubt that people will embrace it in droves, so, again, it is not likely to have much effect on overall supply.
Finally, religious polygamist sects only allow men to have multiple wives. Legalized polygamy today would most likely also allow women to have multiple husbands. That could help balance the supply. It could also provide women a bargaining chip that women in polygamist sects don’t have: “If you go and get more wives, honey, I’ll just go and get myself more husbands.”
My principal objection to religious polygamy is that it makes the practice mandatory, a commandment from God. It is used to brainwash and bully adults into participating, like it or not. Worse, children are raised with the brainwashing. This complicates the “consenting adult” argument, at least when consenting adults have kids. Non-religious polygamy might—might—stand a better chance of avoiding the brainwashing side of things. It would be interesting to see.