You are looking at it from the perspective of what features it makes sense to provide to account holders. Instead, after the SVB fiasco we should be looking at it from the perspective that all bank accounts create liability for the FDIC based on public expectations. As such
all bank accounts should ultimately be "FDIC insured" - not because we want to help out large account holders with decreased risk, but rather because when something does happen, those nominally "uninsured" account holders are going to be begging for a bailout
regardless while spreading panic to get their way.
The insurance premiums on larger accounts should be larger (superlinear) to handle the increased variance of larger amounts. If someone wants to store large amounts of money without (indirectly) paying the FDIC insurance fees, then they choose something else besides a bank account - perhaps a brokerage account and/or buying treasuries directly.
Furthermore, the hazard of bank management gambling the money away should be discouraged through larger capital requirements, and even criminal penalties for blowing through that capital buffer and into customer deposits due to not employing proper hedging or insurance.