At least one of these shows a basic misunderstanding on your part. You say: "[bank account is protected by deposit insurance] sounds reassuring and comforting. When you do the math you realize it’s mostly a broken promise. If something drastic happened to the financial system then an insurance policy wouldn’t necessarily be big enough to cover everybody. Placing all your bets on an insurance policy seems risky. It’s worth reading the fine print."

At least in the US, this is not an insurance policy (implying there's an insurance company behind it, with possibly a reinsurance company behind that, which if something bad happened to a lot of banks could end up failing to deliver on the promise). In reality, deposits of up to $250k per depositor per institution per covered asset category.

According to https://www.fdic.gov/deposit/deposits/faq.html, "The FDIC (Federal Deposit Insurance Corporation) is an independent agency of the United States government that protects you against the loss of your insured deposits if an FDIC-insured bank or savings association fails. FDIC insurance is backed by the full faith and credit of the United States government."

Thus, at least in the US, and up to the FDIC coverage limit, our bank deposits are ultimately guaranteed by the "full faith and credit of the United States government."

Can the US government default on that promise? I'm sure there is a tiny, non-zero probability of that, but (a) that likelihood is indistinguishable from zero for any reasonable individual decision making, and (b) if that happens, the loss of your bank deposit is likely the least of your worries.