While I can see that somewhat, Arabic and Asian literature is replete with instances of it not working out, especially with the junior wife being oppressed by the elder ones, or the senior one being neglected in favor of the new younger hottie. In our own cultural context, most of the women who seem to be interested in it seem to be more interested in the man still being the primary breadwinner without the women themselves being professionals outside the home, which spreads the household resources that much thinner than with a couple...though thanks to our bizarre social entitlement system, they may be able to get benefits as single mothers and so artificially (And fraudulently, to my mind) collect a bunch of gubmint money to make up the difference.
That was exactly the issue with Tom Green, a member of the fundamental "sect" of the LDS church (officially denounced and not recognized by the mainstream LDS church).
While the mainstream LDS church officially renounced polygamy/polygyny as a condition to Statehood back in 1896, the fundamental portion of the church never really went with that flow. As a result, polygyny still is practiced by the more fundamental sects, which are scattered in the western U.S. to include towns like Hildale, Utah, and Colorado City, AZ. They're also up in British Columbia.
More to the point, the case of Tom Green was predicated on bigamy (he was quite loud about his multiple wives), child rape, and money extracted from the state in the form of welfare. He did not work. This was a guy who had 5-6 wives and something like 29 kids and relied on his "wives" filing for single mother welfare. He was eventually tried and convicted of 4 counts of bigamy and one count of failure to pay child support, and one count of child rape.
So besides the cultural issues, the state of Utah (in this case) is forced to look at the fraud part of polygyny, not to mention the child rape thing as well.