Most prevalent Tier 3 raid bosses

All the necessary data is listed on this site but I'm not sure if anyone has compiled it into a useful form. The first raid boss rotation skews the results a lot if included since the originals stayed for months before the first change.

With the exception of the shuffle for Regice as well as events the raid bosses usually serve as counters to whatever legendary is available. That said here's my opinion on a few select bosses:

-Machamp has so far been the most prevalent raid boss having never been rotated out - not even Tyranitar or Magikarp can say this. Should be an obvious target.
-Gengar would be another one I'd prioritize for since it's fairly easy to solo and makes a good glass cannon even without Shadow Claw.
-Alakazam hasn't been around for a while and faces competition from Espeon for best non-legend Psychic attacker, which has slightly less attack for slightly more bulk and uses much fewer resources to obtain. It's also a tougher T3 to solo which could turn some people away due to fear of failure. That toughness also makes room for bragging rights should you be able to solo it, especially Confusion variants.
-Jynx stuck around longer than I anticipated, and while it's not present now it made for a different challenge since it requires different counters than most raid bosses. It could be one to build a team for, if nothing else as an excuse to power up some fire types and that Metagross that's collecting dust.
-Omastar's usefulness hinges on moves it can no longer learn and has been outclassed by SD Tyranitar. If you want to test some grass types against it then go ahead but I wouldn't focus on it.
-Aerodactyl is another maybe, being an easy solo and providing a shiny chance. M-Aero is predicted to have the 2nd highest rock-type DPS assuming it gets the right moves to do the job.

Any raid bosses beyond that would come down to personal preference or needs imo.