I think foul shots at the end (or "foulathons") are actually exciting ways to win or lose games. It's like kicking a field goal in football - it's one of the skills that your team needs to have. And even if you miss those free throws, the other team still has to score. Sure, it's frustrating when you're on the wrong side of it (I have no sympathy for Illinois, but damn, the way they lost to Penn State last week), but it's just part of the game.
If I recall, the 2008 Memphis team was an absolute juggernaut led by Derrick Rose. They had one Achilles heel - they shot free throws poorly. It usually didn't matter because they blew teams out, but in the final against Kansas, they blew their lead because they couldn't do it and KU made the key shots they needed to make to force overtime and win it. Them's the breaks.