They needed to fail.
I'm not a proponent of the LDS church. The organization is a dreadful, terrible thing. It preaches homophobia, sexism, and misogyny. The sects that practice polygamy are worse.
I don't object to the concept of group marriages. If you can manage multiple spouses, go for it. I do object to the LDS version, however. "Reguar" group marriages aren't based on gender, or the ones I know aren't, anyway. The group decides as a whole who should be in it and who should not.
However. The LDS version of the above says only the man can marry multiple wives. Women are not allowed to marry multiple husbands. The man ultimately decides who enters the group. He also makes the decisions for the group. (And no matter what you may see on SISTER WIVES, that is indeed the way it works.) This is misogynistic, sexist, and abusive.
The LDS have argued that polygamy (one man, multiple wives) is a part of their religion, and the government's refusal to recognize these marriages (and Utah's outright ban on them) amounts to religious discrimination.
When the government responded that current law states you are perfectly free to marry one person of your choice, the LDS shot back, "You let LGBT people marry the way they want. You need to let us marry the way we want."
Sorry, no. The cases aren't even close to analogous.
The LGBT community didn't argue on First Amendment grounds to get the bans on same-sex marriage overturned. They argued on equal protection grounds and gender grounds. The LGBT community also didn't argue that marriage laws be changed, only that they be extended to include people of any sex and become compliant with anti-discrimination laws already on the books. The LDS wants an actual change in the law, and there are no grounds for that. The law doesn't forbid them to marry based on their religion.
Additionally, the LDS version of group marriage violates the equal protections clause of the Constitution, since it would extend a right to men, but not to women.
If the LDS wants polygamy to be legal, they need to get marriage laws changed. They'll have an uphill battle, though. Utah's frank ban on polygamy was passed to "prove" that the Mormons were no longer practicing polygamy (but of course all that happened was that it went underground), so there's zero chance of getting it changed at the state level. Other states simply aren't interested in it. In order to have any shot at all, the LDS would have to get marriage laws changed to allow group marriage regardless of gender, and I can't imagine the Mormons arguing to pass a law that would allow four men to marry each other, or one woman to marry three guys. The challenge seems unsurmountable.
And so the Supreme Court stopped a group of sexist, misogynistic fanatics from having their way. Go them! And go all the other judges who rules against them!