Is there a way to bring down the Thieves Guild in Riften?

Although there's a way to bring down the Dark Brotherhood, there is no similar quest or quest line to bring down the Thieves Guild.

On the other hand, there's no disadvantages for joining and completing the Thieves Guild quest line - only benefits, achievements, and advantages!

There is a mod on Skyrim Nexus called WIP - Destroy the Thieves Guild. The author has made significant progress. He even has made a new NPC for the No Stone Unturned quest. I suggest you check it out. It also involves Maven, who you should accuse her or her treachery.

As far as I know there is no way to bring them down. You can choose not to join them "because it's breaking the law" and the dude will tell you if you change your mind to come and talk to him. So you don't ever have to join them at least.

You can drop the ring after stealing it to complete the quest yet avoid the dark elf from being arrested, but I agree, I sure would love to clean Riften from these rats :-(