Your math is way off. More like $50k for 20 million people.
I wrote up a proposal whereby the lowest appraised 20 million owner occupied homes in the nation would have $50,000 placed in accounts to pay the mortgage only, for however long it lasted. If your mortgage was $1,000, it would last 50 months. If you sold the house in the first 10 years, you had to pay back the $50k out of it. If you stayed 11 years, you got to keep 10% of the $50,000, pay back the rest. If you stayed 20 years, you got to keep it all.
The point was to relived troubled assets, not troubled bankers. So, whatever you were trying to do in terms of paying your mortgage, that money, yours, would be saved or pay other bills or whatever but, at least then the trillion dollars would go into the economy and the banks could earn it bank instead of paying it into banks who would then just sit on it.
TARP is simply one of thee dumbest ideas ever IF the idea was to help the American people. It was great if the idea was to help banks and insurers.
That would have cost taxpayers 20 to 50 times what TARP cost them, and that's including all of TARP not just the primary aspect of it which was meant to save the economy from imminent collapse. That primary aspect I'm referring to didn't, in the end, cost taxpayers money. It ended up being profitable - i.e., the banks which were used to get the liquidity into the system (because, e.g., they were the only feasible way to get the needed liquidity, and more to the point confidence, into the system quickly enough) ended up on-net paying for the privilege of being used to save everyone (including, to be sure, themselves with regard to some of them; but also most Americans for the same reasons and who needed saving, whether they realized what was coming or not, for much the same reasons - cascading counter-party defaults).
The aspect of TARP that actually cost taxpayer dollars is the aspect most similar to what you suggest - the program for writing off portions of certain people's mortgage debts. That's the part of TARP that other people paid for, that's the particularized bailout aspect of the situation - the part meant to help particular entities and which cost other taxpayers money. (TARP cost us all in other ways, I hope I don't need to qualify what I'm saying by reiterating that I think TARP was a mistake and I'd have preferred we gone a different way.) The auto bailouts also cost taxpayer's money (not even considering the somewhat fishy tax loss carryover aspect of them), but that amount was largely offset by the profits from the bank bailout aspect of TARP such that the total losses from TARP are roughly the same as the total losses from the mortgage relief aspects of TARP. Further, the AIG bailout probably cost us money, but that loss was more that absorbed by the bank bailout profits.
All of that aside, what you suggest - while costing us an order or two of magnitude more than TARP did, and infinitely more than the bank bailouts did - would not have fixed the problem. What was needed was immediate liquidity (in reality, the confidence creating assurance that such liquidity would be provided to the extent needed), injected centrally into the system such that it got the blood flowing again - or prevented it from stopping altogether - throughout the system. Making some money available to millions of tiny capillaries, hoping that enough of that money would find itself flowing into and through the system at large quickly enough to make a difference - to prevent the effective seize up of the system - wouldn't have accomplished what was needed. It would have been a nonsensical way of dealing with the immediate problem that was faced.
This was about acute systemic, self-perpetuating, insolvency - money flow, which is the lifeblood of a modern economy, was seizing up. Right then, not in a month or a year. It wasn't about substantive economic losses (those existed, but they weren't the problem that was being faced - it wasn't that certain big banks were going to suffer major profit declines or losses; they did so but that wasn't what jeopardized the entire system and what the bailout was meant to fix). It was about people and entities stopping handing money from one to another, a dynamic that fear perpetuates - sometimes quickly to the point of causing a catastrophe. And in our system, when money stops being passed from one party to another it effectively ceases to exist - at least, that portion of it (which is huge as compared to, say, the base) which really only exists by virtue of it being passed from one party to another and thus, for practice purposes, appears to be in several places at the same time. That's really how money is created, it is loaned into existence - it is transactional. Without the transactions, without activity - to include the daily process of paying back what is promised - the money disappears. Individual people don't move enough money around quickly enough such that putting money directly into their hands can quickly recreate the needed flow, the needed transactional money, the needed liquidity. They aren't connected to enough parties as directly as the big banks are. That's why the liquidity injections had to be done through the banks - central lines, not capillary taps.
And, at any rate, we couldn't just do what you're suggesting with the money instead of what we did do - one is spending the money, giving it away; the other is loaning or investing it, getting it back for the most part. We could still do what you're suggesting, it would just have a real price tag and - I think - exacerbate the big picture problem that both you and I see with programs such as TARP. We make failure, we make mistakes less painful and thus encourage it - we encourage reckless behavior and make parties less accountable, individually, for it. It's what you've described before - privatized gains with socialized losses. Those people got the benefits of their recklessness (or miscalculations) and society is asked to bear the cost of them. Better to let individual parties suffer the consequences (as well as reap the rewards) of their actions and re-build a society on that prosperity-facilitating bedrock, on that concept. Now, we likely aren't going to meaningfully get back to that. But what you suggest is a further step in the wrong direction. It isn't wiping the slate clean and starting over, it's reiterating the paradigm an reinforcing the mindset that is in large part causing the problem.