I'm just curious if rotaries will see any benefits from dumping a bottle of fuel injector cleaner into the gas every 3000 miles or so. Doesn't brand name gas like Chevron or Shell already contain something that'll do the job?

Yes, gasoline already contains detergents, brand depends on how much and what. A min is set by the Gov. An injector on a rotary is as likely or more likely to become dirty as a piston engine, so yes injector care is equally important on a rotary. If you're running premium fuel and stretching the legs periodically you shouldn't have a concern for many miles. If you do a lot of freeway driving and dont run it to redline often it may be more of a concern.

I also think that the cleaners might help with carbon buildup in the chambers the rotors create as well, hopefully keeping it soft enough to blow out, but that is just a thought.

I stretch the legs quite often :D

What does the owner's manual say about this?