It's weird though. Significant chunks of both the Gamma (Dominion) and Delta (Borg) quadrants have probably been "brought under control" , yet no indication of any godlike being taking action -- only when they crossed the wormhole into the AQ (and Sisko had to plead for that). Does the Alpha Quadrant have a special place in the heart of godlike beings, and don't they care about these other quadrants? (Oh, and by 'godlike beings' , I'm not referring to the writers).
Yes. Even just in the original series, the Enterprise met the Organians and Trelane's species. Then in TNG we quickly met the Q and the Borg. Why don't godlike beings hang out with the Founders sometime?
Not that I think any of those godlike beings are interested in being the cops for the Founders and other non-godlike species. That would be like humans trying to referee a fight between rival colonies of fire ants. It would be low on the list of things they care about.