Flogging the dead horse, but hey, what the hell, he's in a better place now. ... Anyway, it does seem that the game could prompt the player to buy more balls when down to 1. Now you have to deliberately go into the pro shop in another window, which is somehow counter-intuitive (as one player in this post, for example, wasn't even aware you could do that).
Bottom line, though, getting switched back to the starter ball is something every player learns once on the WGT, the hard way, and then it doesn't happen anymore.
The one-ball stipulation is not an ordinary rule of golf, but may be imposed for certain competitions. In ordinary play, there is nothing preventing players from switching balls between holes for any perceived strategic advantage.