Here are some thoughts:

1. It's certainly possible. It could also be that by the time they rebooked you all the better flights were taken by people ahead of you in line or had rebooked in the lounge/phone. Your airline may have been less willing to put you on another carrier because of lack of status/low fare.
2. They'll generally try to keep you in the same cabin. Though they may offer you a quicker flight in a lower cabin. A few months ago I had a flight to South America in AA Flagship First that was delayed 15 hours overnight. They offered me a seat on a flight a couple hours later but with a triple downgrade as there were only seats available in coach (I didn't take it).
3. Airlines have agreements with each other that cover how much each gets paid when they send passengers over.
4. Some locations (e.g. EU/UK) have compensation schemes that cover delays/cancellations. The US does not, so any compensation would be a customer service gesture.