MIT had roaches for the same reason most urban spaces had roaches: there were plenty of things for a roach to eat. In addition, the roaches bred faster than we could kill them off. They knew how to get into any space, and their adaptability made them indestructible. We did not have medicine cabinets in our dorm rooms, just open shelves, so roaches could get into our toiletries. Fortunately, we had dresser drawers, so we never found roaches in our personal effects, although I did end up squashing one inside my sneaker once (yecch!)
The cockroach is one of those creatures, like the shark, that has been around almost since the beginning of time and will be one of the last creatures remaining on Earth when it gets swallowed up by the supernova-ing Sun. In fact, if Christian potboiler novelist Tim LaHaye wanted to be factually accurate, his end-times milieu would have an Earth inhabited by nothing but sinners - and cockroaches.