There are three major strikes against the idea:
1. Marriage and divorce laws are complicated enough with just two people; adding the possibility of more turns it into a potential nightmare. You can sidestep some but not all issues with out-of-the box thinking, but that would require major rewrites of how marriage law works. Same-sex marriage only required minor tweaks which don’t fundamentally change anything.
2. Support for poly marriage isn’t there yet and won’t be for a good long while. The vast majority of conservatives are against it because of the whole one-man-one-woman thing, and liberals fear what patriarchal religious cults who don’t subscribe to one-man-one-woman might do with it. Meanwhile there’s the general perspective that being in a relationship with more than one person is “selfish” or “greedy”, which is a fundamental misunderstanding of most poly people’s motivations and their approaches to relationships.
3. The number of stable, long-term poly relationships appear to be tiny compared to two-person same-sex ones. I say “appear” because it’s not clear how common it actually is, since few people are open about it outside of alt-culture communities. Or for that matter, how common it would be if there wasn’t so much social pressure against it. And it’s not like they’re being purposely or openly oppressed (like, say, trans people) or that there’s anything like a civil rights movement for poly people, so it’s not exactly a high priority even among those who fully support it.
So… while I do expect poly marriage to be a thing in at least some countries eventually, we’re still decades away from it being tackled as a serious issue. Hell, I suspect that decriminalizing public nudity would come first in most places. And I would not at all be surprised to find that the first nation to do so wasn’t even on Earth.
- TL;DR Much as it would probably be a good thing if done right, it’s definitely not on the horizon. Maybe for those who are scared of it happening and have basically no other fears for the future it would be reasonable to work towards preventing it from ever coming to pass (for a certain value of “reasonable”), but otherwise, the sky isn’t falling.