Even the USGA will eventually figure out that the stick provides at least a marginal advantage, and that more than speeding up play is going on. Even an organization of guys who love to ignore data AND common sense will be unable to ignore this.
Wow, talk about being lost deep in the woods!
If the flagstick rule is changed it will be because the "data" suggests that the benefits (speed of play, mainly) did not outweigh the costs (a clear advantage- putts going in that would otherwise run past the hole). Mind you that developing convincing numbers will require studies with extremely large number of trials to evaluate many variables (15+ come to mind quickly). Personally, I doubt that a study will conclusively answer the question, especially if a significant advantage standard is required to once again modify the rule (for a decade or so prior to the late '60s, the 2019 flagstick rule was in effect).
Anecdotally, in the 13 rounds I've played this year, mostly with the flagstick left in, I've had one putt affected, hitting the right-center of the stick at moderate speed and glancing off the lip, around the hole and out the back. Had the stick not been there, we all had 0 doubt that it would have gone in. I don't remember anyone else's putts being helped or hurt by the flagstick during those rounds.
One upside of the new rule is that the flastick doesn't get tossed around the green or otherwise mishandled as much. We have a couple guys who like to have it tended from 20' in, and we typically just hold the stick while they putt and then put it back in.
A downside is the potential damage to the cup in trying to take the ball out of the hole with the flagstick still in. Guys who wear a glove or have large hands seem to have the most trouble.