ubiq: Until Rabbeinu Gershom, the people married to more than one wife were regular Yidden, not any special circumstance such as a king or people who necessarily couldn’t have children. In fact, R”G made provisions when establishing his Cherem to provide exceptions in special situations such as inability to have children. [i.e. See Darchei Moshe (Even HaEzer 1), Rema (Even HaEzer 1:10)] Beforehand, no special situation was required.
With the Teimanim, Morrocans, Sephardim and non-Ashkenazim who practice polygny right into the contemporary modern era, it is also regular Yidden who practice it.
In any event, if the Ashkenazic Gedolim reestablish it in present-day times for Ashkenazim (non-Ashkenazim already have the natural halachic right to practice it), they could institute it with guidelines on who is or isn’t authorized to do so. Such as requiring the husband to have the financial wherewithal to support multiple wives and/or other criteria limiting it (i.e. the acceptance of his current wife/wives.)