Oh, it happens. The airlines call the seat selection a "seat preference". Passengers have been bumped before, especially if there's a frequent flier paying full fare. United says a schedule change, equipment change, or "unforeseen circumstances" may result in a seat change, and that seat selection isn't guaranteed. It's the "unforeseen circumstances" that may include all sorts of things such as keeping groups with children together or the frequent flier.
I've flown hundreds of times but I've never seen some random family bump me out of a preassigned seat just because they wanted to sit together.
There are a number of ways this might happen, and one was mentioned by a previous poster, that the "selected" seat was noticeably different upon check-in. Another is that once on-board, the flight attendants attempt to shuffle around passengers, especially if it's a special needs child or a particularly young one. My wife has asked before flight attendant intervention was needed, and they've almost always done it rather than endure sitting next to a four year old without a parent. Often the flight attendants will offer something like a refund of any seat selection fees, free drink coupons, or vouchers. It could potentially escalate to an order, although that's rare. This is nothing compared to a train. I know some people like having two seats to themselves, but of course once the attendants need to shuffle passengers to place groups on the same reservation together, they will.