I need max. 15 seconds to unlock the bike and start riding it. You say you can't be 30s faster on a bike than someone travelling at walking speed, even for short distances? I guess you can't only if it is 30s walking distance.
If you're more than 2-3x faster than pedestrians, you're a danger unless you're separated from them, and bicyclists are rarely separated enough on a college campus.
1mph is 264ft/minute. Reasonable walking speed is about 3mph, or over 750ft/minute. A safe bicyclist will cover that distance in about 20 sec, saving at most 10 sec.
Meanwhile, the walkers had a conversation.
And, since students have 10 minutes between classes, the time saving of faster transport doesn't buy them anything even if they're going 1,500ft..
That's why students who own bikes don't use them all that much. They're only useful to/from campus and for long-hauls.
Also, bikes need more maneuvering space than pedestrians. Not as much as rollerbladers, though. (Don't get me started...)
The majority of college students who walk between classes have bikes, so why would the availability of free bikes change their behavior?
Bikes are probably best suited to trips of about 1/4 - 10 miles, alone, with less than fifty pounds of cargo. (That covers more trips than many people realize.) Riding a bike three blocks is probably not worth the trouble, and riding fifty miles is (while quite possible) going to take a few hours.