I think it predates that, actually, slapout. I would take it back to Root's changes in the personnel system around the turn of the 20th century as well as the expansion that we undertook for both world wars. Root's changes created the trend toward modular manning (individual replacements and the generalist officer) that we see now, and the expansion for both world wars saw men shuffled around as cadre and filler for new units as they were created. Someone also figured out that it's "cheaper" to move a flag rather than an entire unit when it comes time for station changes and the like.

There were certainly some downsides to the regimental system as it was practiced by the Army prior to 1900 (an ossified promotion system was one of its biggest downfalls). I'm not sure, though, that the new system is much better. What we gain in flexibility and supposedly more skilled officers (although I'm not a huge fan of either "up or out" or "generalist" officers who are incompetent or at best semi-skilled in a number of areas but really knowledgeable in none) we more than offset by a loss in unit cohesion and tradition that can serve as a good service totem for our troops.