What's wrong with just letting the companies fail?
Short answer- you could end up killing millions of people, and that isn't a joke.
Forget high finance sector and executives making millions in bonuses- how are you going to buy a gallon of milk or a loaf of bread?
You may have millions tucked under your mattress at home, companies don't. I work in distribution, the company I work for has over a billion in liquid assets which are utilzed as a credit line to move product, we have had one quarter with a loss in the last ten years(we have been quite profitable even in the current situation)- but if the banks were to fail outright, my company shuts down. Given, we just distribute- but one of the items we distribute is grocery products(we handle everything from jars of baby food to TVs and pharmecueticals).
Banks go under collection of food stops immediately- companies have no funds available to purchase. Collection of food stops, production stops at all the food manufacturers(Kellogs, Kraft etc) shipments from the manufacturers to the distributors stops(that's me

) and shipments from distribution to store level stops. The amounts of money we are talking about moving are several billions of dollars per day(nationwide, not just my company), yes our liquidity is not tied up in a bank account, but being able to turn the liquidity into moveable product we need a very large bank to back it via a credit line.
The amount of time it would take to build a new financial backbone for the amounts of dollars we are moving under normal circumstances would take years, but let's say we get some insanely fast movement by the government and large corporations and that got trimmed down to one month. You would have a one month gap with no production of food products. I'm not sure what most people think that stores carry for on hand inventory, but two weeks worth of product is the norm for a grocery store(about 8-12 weeks for retail). Half way to getting a system put in place all of the grocery stores in the nation would be out of food. Due to regulations, I honestly have no idea how long it would be before medical supplies dried up, in terms of scripts(government regulations don't allow us access to store level inventory on those items for numerous reasons), but I can tell you that most of our customers get 3-4 deliveries per week, so it can't be too high.
So, letting banks fail has you about two weeks out from not being able to buy any food. If some things got worked out in a month we could clear the channel of what we had left for inventory(which would give you about another two weeks for staple items, far more if you want to load up on hot sauce and marinades

). Two weeks without any food would thin out the population a bit, but you would still be dealing with roughly a month to get production back up to speed- probably would be a few more days worth of inventory that the producers had on hand that we could push out to the populace, but you still have about a week delay transit time from when the wheels start moving again until when you are able to actually purchase goods from a grocer again. So about two weeks with food, two weeks with none, a week maybe two with some, then about three more weeks with none.
Planning on eating out- restaraunts will run out of food long before the grocers will
This is not paranoia, this is what I do for a living. The banks failing was never a viable option for the powers that be, we need them as a functioning society far too much. If we had another way to move large amounts of cash very quickly it would be a bit different, but we don't. Consolidation and the large corporate structure of the US business world demands we have large banks backing our credit lines or everything falls apart. I don't think it is wise to bash the corporations for being so dependant on the system, what happened if you got up tomorrow and there were no roads when you were going to work? Same general idea on how fvcked we would be if the major banks all failed.