1. Picture a complete freeze in lending, and a lack of access to cash. No one can buy cars or houses. People with no cash on hand couldn't buy anything. Stores can't stock shelves or pay employees. Forget just the banks, every company from GE to local mom and pop shops would be under within a month. Tens of millions would suddenly find themselves out of work. You'd have mass riots in every major city in the nation. If we were lucky, we would be living in a state of martial law.
This entire premise is based on the fact that new players will not enter the space that just appeared.
Riots? Martial Law? You have got to be kidding. This reeks of statist fear-mongering.
Not even the great depression brought on Martial Law.
2. And as for your ridiculous solution, is this something you actually spent more than 2 seconds to think up? Honestly, how long do you think it would take for the government create this plan, to identify these people, and to mail them checks. A few months? A year?
As opposed to giving reward to the stupid and losers? Now that was ridiculous and down right evil.
And as for your time frame, there is this tech called a database that Dr Codd nailed for us in 1969.
As a real world example, the Australian government gave out $800 dollars to every tax payer directly into their bank account within 3 weeks. It's not hard.
It was a perfect Friedman helicopter drop. Minimal implementation cost and only a few dead people wasted it.
3. What money was spent? In the end, the banks paid the money back, so what money could have been "saved" for a better use?
The opportunity costs that the US lost by keeping the dead wood alive is immeasurable. You are currently experiencing a "long slow painful recovery" due to propping up zombie businesses.