Why would Mizzou decide to quit playing for 10 minutes against a rival? Illinois is not a good team.
You answered your own questions.
Mizzou let up because they knew Illinois couldn't hang with them. Lots of teams do it. The thing about Illinois, though, is that they actually do have quite a bit of talent. Of the ten guys they played, eight were top 150 recruits (and another was a pretty good three-year starter at the mid-major level). They played three top 40 recruits for most of the game, and two other top 50 freshmen haven't even cracked the rotation yet. Whether or not they're a good team, they do have plenty of individual talent. And when you quit playing against a team like that, they can get back into a game.
And let's not act like Bruce Weber is some kind of coaching idiot, either. Yes, he did it with Bill Self's players, but this guy did play for a national title. He had been a successful mid-major coach before that.
Regardless of whatever flaws Illinois has, I don't think BYU or Davidson are better teams.
I'm not saying MU will win anything based off tonight's game... just that you can't do the opposite, either. Mizzou did not play well, but they're not the only ones who have had games like this. The two teams you put above Mizzou have had arguably worse performances against lesser competition.