Tell Me Why This Can't Work

I am not an economist, nor am I a financial wizard, but I wonder sometimes if the simplest solution might just be the best. Some of the people in trouble with their mortgages may have overextended themselves thinking their house value would go up or their income would increase. What then happened is an adjustable rate mortgage adjusted and the payments are too much. At the same time, they cannot sell since they would have to come up with money at closing. Maybe they even anticipated refinancing but could not since they owe more than what the house is now worth in this market. Why could they not re-amortize what is still owed over 35 or 40 years? Payments would go down at least a little, and if they stay in the house for ten years or more, they may be able to eventually sell at better than a loss. The lenders would continue to have income and the collateral, the homes, would have an opportunity to gain in value so that the loan to value ratio might actually improve over time. The only place I see in this scheme for any government bailing would be to bring some of the ridiculous A.R.M.s down a point or two.
Folks who invested in houses just to flip them in a year or so for a profit would not gain by this plan, but they are really in business rather than occupying a primary residence. They are not my concern.
People might have to stay in "starter" houses a decade instead of a couple of years, but wouldn't that be better than suffering foreclosure or spending my tax money to save them from bad decisions they may have made?
Then we look closely at when and how we got into this mess. Who thought that 100% financing was a good idea? And about this bundling of mortgages to spread risk. . . it got spread right into all of our living rooms. Let's look long and hard at the regulations over the past 10+ years and make sure the congresspeople and other decision makers who were in the lobbyists' pockets have to look for other work soon.