You know, what I've been considering about the Thieves Guild is that even if you don't help them, another guild would arise that you wouldn't be able to kill unless you're in the guild. Unless we delve into fanfiction and mods with options such as killing the Thieves Guild, then you would either join, or let them fail. Now, if they fail, then most of them either go solo, die, or join another guild of Thieves. One of the TG quests is to take out a rival guild, the Summerset Shadows. Now, if you don't join the TG, then they might theoretically expand, and possibly take the TG's place. In addition to this, if you don't join them, then Mercer gets away with the Skeleton key and gains an insane amount of power with it. However, if you do catch him, thieves get their luck back and become more successful. I'm having a tough time deciding whether or not to do it. If you kill the DB you don't miss much if you've done it another profile, but you miss a lot from the TG.
I wouldn't place any bets on the Shadows. There's nothing really suggesting they're going to expand. For a morally good character (delving into the meta game) Mercer escaping is much better than the guild being restored. That whole situation is poorly handled in my opinion. Nocturnal is either blind or some kind of weird sadist who is rewarding Mercer for stealing from her, and punishing the unaware guild /tangent
If your objective is for the character to do the most "morally right" thing, then don't join the guild. It will, as you said, probably die out. Maybe it gets replaced, maybe it doesn't, but you have to meta game real hard for that to be your character's fault.
Justifying a character is easy. It's justifying the guild that's hard. For a single character; make them impoverished, an outcast, starving like Gentleman Wolf suggested. Joining the guild becomes about survival. Staying with the guild becomes about repaying a debt. There's really no good way to look at restoring them, though.
You know, considering that my character hasn't even met the Greybeards yet, I might just go with the idea of him trying to dodge his fate. The Thieves guild works in the shadows, so him joining would make sense with his goal of trying to hide without falling to the level of the Dark Brotherhood. Considering how the quest line ends, I might have my character go through the Companions, Mages Guild, and Thieves Guild until he realizes that he has to embrace the fact that he's Dragonborn.