Specifically on the Center position, today's players feel such a label is too limiting and I guess if there is ambiguity in being called a guard or forward, most players would rather see themselves described as a guard. Again, viewed as less limiting.
Agreed, this may be more of a players than coaches trend. It has little to do with how they will be used in college, but is more of a reflection of how the player wants to be portrayed. Calling yourself a center suggests a one position low post player. In addition quite a few players go smaller in position as they go up in competition. If they have WNBA or European ambitions they want to be viewed as a good prospect one position or more smaller than they played in college. In it's extreme you have a player like Gabby who played mostly PF at Uconn but also guarded the other teams C on occasions, and last year she rightly or wrongly was used at PG for the Sky.
Some SG's and SF's in the WNBA were probably their teams center in HS, for example. More trends in labeling are any big that can shoot from the perimeter wants to be called a stretch four or five, with traditional post players almost being viewed as limited. The 3 and D designation is so much more common as well, suggesting a possible good two way player, even if the offense is limited to spot up threes.
I'm not sure, but it seems to me that coaches used to judge a player's best position on who they could guard, more from a defensive standpoint. That generally meant a closer match in size. Big differences there often produces more offense on both sides. The bigger player can't keep up with the smaller one on the perimeter, and the smaller one gets taken inside and posted up on the other side.
Over time the 3 ball has increased in importance tremendously. One or two three point shooters were enough. Now the best teams expect their SF to have three point range, and hope they can find a big that can do it as well.
Instead of lineups matched more for size and defense, more of an offensive skills match with less regard to size. The traditional C hasn't disappeared, at least for their traditional defensive stopper and rebounder role, which is still badly needed with small ball. The PF and SF roles, however, have evolved quite a bit with more emphasis on small player skills, and players want to be though of as having those skills in my opinion.
