Guys have been annealing bullets for a very long time - I learned about it as a kid over 30yrs ago, and it didn't seem like anything new even back then.
No change in flight behavior (at least as accurately as I've ever been able to shoot), so I shot with non-annealed bullets to practice, then stashed a few boxes away for hunting.
Wouldn't ever do it for prairie dog blasting, but for big game or coyotes where the annual shot count is low, it wasn't that bad.
I WILL say, the guys who taught me to do it always did it with loaded ammunition, to eliminate potential for tip deformation during seating. Not everyone is comfortable with taking a flame to loaded rounds.