It's cheaper to write down the asset (the loan) and bring it current than to have non-performing loans or repossessed collateral.

Actually, this is supportive of real estate values -- the real estate was worth
less than the loan anyway so what's the difference?

The difference is that the loans become performing assets and the real estate doesn't get dumped on the market -- that would depress values further.

At some point you have to take a loss when you see there is no recourse.

Greece's bondholders get the drift ...