This isn't like FTX where your "assets" are worthless IOUs written to yourself.
The bank has assets. Just not enough to cover all liabilities. That's why you see the term "haircut" being used a lot in these threads.
1. FDIC insurance only covers $250k. FDIC insurance is mostly to reduce personal risk, so individuals feel comfortable keeping their own money in the bank. This is key to the banking industry because individuals are much more likely to horde physical currency than businesses are.
2. Who would insure the bank for unlimited deposits? If it's a non-governmental organization how would depositors know the insurance company is good for it? If it's a governmental organization then the taxpayer would essentially be a codified safety net for corporate risk taking. The insurance is more political palpable (and affordable) if it's seen as protecting individuals from bad banking practice then if it's seen as a bailout.
3. Banks ideally are the safe organization to hold cash. A bank failing is seen as a failure not only for the individual bank, but for the set of regulations that banks must follow. One bank failing reduces trust in all other banks, so it's in the industry's best interest to accept regulations that prevent bank failures.
Could be some of these companies have other types of insurance against this, but for a lot of small startups this is way down the list of things you'd get private insurance for.
Otherwise no financial institution is actually insured against it's entire book. That would be insanely expensive and financially complicated at the scale banks operated at. For example, JP Morgan Chase has $3.7 TRILLION in liabilities on the books. Where the hell is an insurer going to get $3.7 trillion to gamble?
Even if each owner had all 14 types, they only get $3.5mil in insurance. And the bank has, allegedly, somewhere around $200bil in deposits.