Yeah, not gunna happen. the problem is that in an effort to protect the players, refs blow the whistle quickly - if we did what you recommend with the way the game is called today you'd end up with a 3 hour game with a jump ball every couple minutes...or one that had 16 technical fouls for hitting guys with your elbow trying to prevent a tie-up. Not saying its a terrible idea, just that there's a huge ripple effect on how games would need to be called that needs to be taken into account.
Personally I don't mind the alternating possession, I think older fans fondly remember the jump ball as a much better idea than it actually was. A jump to start the second half makes sense...not really down with any more than that.