Don't think this works at least in Europe due to regulations. Due to some kind of error, I was bumped from from a flight a year ago, which meant I a) got a free flight the next day b) got the cost of food and a hotel for the night back from the airline, and c) around 80€ flat.
So unless you absolutely have to be there the day of your flight, it is even a pretty good deal to stay.
The cash compensation in Europe if they bump you is 250 - 600 EUR per flight and person, depending on distance. That even applies for significant delays.
To be fair, it can be a hassle to get it. But sometimes, if the airline is clearly at fault not.
And for the record: Every airline overbooks. But usually they find enough volounteers to make it work.
So unless you absolutely have to be there the day of your flight, it is even a pretty good deal to stay.