What about an end of game scenario, where teams foul to extend games? Should the team that is leading be able to decline the foul? It would greatly speed up the end of games, but limit the ability to come from behind late. Also, you'd likely see some very hard fouls from trailing teams trying to steal the ball, since they have nothing to lose if a foul is called, but everything to gain if they're successful or the refs let contact go.
I'd propose that teams can decline free throws on off-ball fouls, but the shot clock resets and the player committing the fouls is still charged with one. But if you foul the player with the ball, there are still free throws if you're in the bonus. If you can touch the ball, you need to be able to make your foul shots.