Do you think most entities socialize the cost of their finances by just dividing up millons to billions between infinite banks and customers of this bank are the only ones not doing this? This seems unlikely. What you are proposing would obviously cost more money in practice else it would make no sense for you to propose it.
Lets take it another way. Why not limit FDIC insurance such that its harder to stack them and derive more benefit?
Sure, if we change the limit of FDIC so it's harder to stack that would make sense. e.g. coverage is per entity not per account.
But that's not what people here are suggesting. People are suggesting to divide the funds so that it's all covered. That it was irresponsible of companies NOT to do that and hence they deserve not to get the full deposit amount back.
EDIT: yes it'll cost more money to split today. But it's a waste. The extra cost doesn't go to the FDIC or tax payers, it just goes to a middleman. So then why not just raise the FDIC limit? (or change the rules so you can't split it)
You are oversimplifying their argument. People are suggesting that people use more than one bank or make a service that involves using more than one bank not necessarily infinite banks. It isn't necessary to choose between zero risk and existential risk. You can with only modest effort achieve moderate risk.
the math is still the same though, just different degrees. If we (as tax payers) are ok with insuring 3 accounts (as an example) x 250k each, why are we not ok with insuring 1 account for 750k?
