So long as the members of marriage are all in consent of allowing the additional person(s) into their marriage contract then it should be fine. The moral panic invoked about children is just fear mongering; children cannot consent and thus children can only be involved in illegal marriages. It's also only a problem in the Mormon compounds of Utah because of the very small and relatively closed confines where it becomes difficult to monitor and regulate.
Plural marriage also solves several problems where, in a plural marriage, persons may not be able to assert custodial rights in the case of divorce or death despite being a (albeit non-biological) parent to a child of the marriage. There are also issues with power of attorney and visiting rights in the hospital and so on. I don't see why we shouldn't have it as a legal marriage since it's going to happen anyway, especially within certain religious denominations, and there are benefits to legislating it.
However, I find myself uneasy on the notion of focusing so exclusively on men and 'their' wives, by virtue of the modern marriage everyone in the marriage would be wedded to each other irrespective of romantic status. It also can be in any gender mix as either men or women could have multiple partners of either gender according to their orientation, personal relationship and consent of their partner(s).