"Why not increase the rent to cover the shortfall?"
Probably because rents exist in the real world, not the fantasy world where everybody thinks that real estate can only go up, up, up so they buy more than they can reasonably afford (I'm speaking of the extremely bubbly real estate market in my own city - and several others these recent years). Rents are always tied into the economic reality of what renters earn/can afford/are willing to pay. They realistically won't be able to rent the place out for $450 more per month if they are already renting it for what the market will bear.
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