Completely irrational, you will regret it. Do you actually know anyone who has gotten a bailout or loan mod? I do, and after reading the terms it isn’t what they thought it was, in three cases this has been true. In other cases, no bailout came, they didn’t qualify for a mod, their lender said no or a host of other reasons. For the most part, mods were only available to people who’s proprty lost significant value, not that they could no longer pay. Most programs are for those that got caught with their pants down, not those that want to pull their pants down.
Let’s break down the scenario you presented. You still need at least 10% down, if not 20%. So you will have 80-160k skin in the game, lets use 20% for argumnents sake. the 640k loan has a 4k P&I, probably over 5k with impounds and 6k with utils. At 125k, your take home is less than what it takes to pay for the house and keep the lights on.
Bailout and loan mods take two routes, refinance the current value and hold back the remaining principal for a few years or until it is sold or refinanced, this is designed to get you through a few years and amounts to nothing more than a neg am. The second is using your new income to factor your affordable payment, it’s risky that they would even let you do it, and it’s a 160k risk that you are taking. Either way, you do not build any wealth, you just rent, but pay more than rent.
I don’t know the percentages but I’ll bet more people lose their houses than are bailed out, take that 160k to a casino, play a single hand of blackjack, I think those are better odds.