You stated that "Someone living in that house, however, who doesn't want to move, ... would therefore be willing to make payments to stay in that house that are higher than what you could get if you took the house from them and resold it."

So having just stated that the current homeowner will always pay more than the bank could make on a foreclosure sale, I think you did, indeed, just argue away the existence of foreclosure.

Of course, some people would probably just as happily default, because they're not compelled by sentiment to stay in a place when they could move somewhere cheaper in a time of falling markets, so any bailout plan for individuals would have to address a way to compel those people not to move.