There seems to be an overwhelming consensus here that Microsoft is trying to protect its interests by preventing piracy. This is, of course, true. However, someone above mentioned a mother buying a PS3 instead of an XBox 360 because she was concerned about the banning, etc. The argument then is that Microsoft loses revenue by scarying people away, while all the banned people continue to refuse to buy games. In other words, they see Microsoft taking a net loss on this.
However, aside from preventing piracy, Microsoft is trying to prevent cheating. People are throwing around a number like 99% of people are doing this to pirate games. However in my experience there are as many people who mod in order to cheat in multiplayer games as there are people who do it specifically to pirate. I'm sure that the cheaters ALSO pirate games, but for a large number of people it is not their primary goal.
Lots of gamers will be turned of XBox Live and buying 360 games in general if they encounter a large number of cheaters while playing online. I've encountered more than my fair share. Microsoft gains from protecting legitimate customers from cheaters, keeping those customers playing and buying new games (and XBL subscriptions).