Ideally the idea of an FDIC limit is just removed and banks are just further regulated to ensure that risk is kept at acceptable levels such that FDIC insurance fund is always capable of absorbing any failures in full.

Im not sure thats possible. Like all regulation, it’s impossible for the regulator to truly know the full situation. It would take a massive army of regulators to go through the financials of thousands of banks in the US. Plus the banks can lie, put things in their best light, or structure transactions to make it look like a lower level of risk than there really is.

And of course, by the time the regulator finds out, the damage is done.

I think its far better to cap the risk protection. That way you have customers doing their own risk management as well - avoiding what they perceive to be risky banks, diversifying deposits across banks, choosing alternative assets to store wealth, etc.