I agree with two bikes, one specifically for commuting and one for other stuff. If one is disabled for some reason, you still have the second bike to get around on. But I commute on all of my bikes.
I wouldn't go so far as only riding the cheap bike if you ever leave it unattended. That really depends on where you are, the crime rate, maybe a few other things. The commuter itself doesn't have to be expensive though. See my thread
Dawes Streetfighter review for example, $270 total cost and everything I want from a commuter. Then the other bike can be more specific to what you like in a fun bike, touring, or whatever your criteria are.
Ha, I see you already did that with the Trek from CL. Perfect!