Transaction accounts don't earn me anything and have fees of their own. There's little incentive to stay at one bank over another. If they want equity, they should sell long-term secured loans with LVRs under 100% or lock in my cash with term deposits or any number of other less liquid asset classes. But why should I feel guilt over moving my cash from one bank to another?
Maybe it's because I'm Australian but I feel our banking industry is significantly more stable. The last time a bank had any serious issue was 1990 and it was a (single bank that itself was bailed out by the government). Australian banks make their money through mortgages (averaging less than 80% LVR or insurance-backed if higher and with fixed terms of generally no longer than 5 years), credit cards and management fees on long-term investment products -- they don't rely on investing cash deposits on long-term illiquid instruments.
The fact this doesn't seem to be the case should raise questions over the entire US banking industry. Cash should be liquid.
Edit: For reference, APRA (bank regulator in Australia) has some very strict liquidity risk management requirements and most banks own liquidity requirements are significantly higher than this: https://www.apra.gov.au/apra-explains-liquidity-banking -- an Australian bank would never be allowed to purchase a 10-30 year bond to match against cash assets.