There's nothing stopping _you personally_ from purchasing insurance on your $5m at the bank from an insurer (or reinsurer) instead of socializing the cost of insuring higher-valued accounts on everyone else.

The one thing that mandatory FDIC insurance gives you over purchasing private insurance is a) the US Government is guaranteed to not go bust (and if it does, we're all living off canned goods anyway) and b) you avoid the situation where people don't do the responsible thing and then you have to bail them out anyway (this is also part of the argument behind government provided healthcare insurance, but that's another topic for another day)

Buying private insurance leaves you open to the risk of the insurance company going bust, and, it not being mandatory means people can take the risk and then come crying to the US Treasury to solve this unknowable systemic risk that everyone actually does know about--which we're already seeing heavy pressure from people to bail out these depositors who are above the insurance limits

Yeah people keep saying that but as far as I can tell from googling, there's no such thing as buying supplemental insurance for your bank account. Can you link an insurer that offers that?