>I'd be willing to pay a fee to the bank to hold my money for me.

You are effectively doing this already (twice). Perhaps your bank charges you a yearly fee for the account in the likes of $10/year, but you're also "paying" by not investing the money yourself, of course, the bank has many lending opportunities that you have not so you might not be capable of doing so. But the point still stands.

You can pay them for a safe deposit box and they can properly _hold_ your money if you want, but that money won't be worth much in 30 years.

Unless I'm wrong and some banks provide a fully backed savings account? Doubt it would be worth the effort for them.

Depends on what your threat model is. A safe deposit box is safe from bank collapses/bail ins, but not against theft.

>but that money won't be worth much in 30 years.

In that case you'd probably be stashing gold rather than bills.

>Unless I'm wrong and some banks provide a fully backed savings account? Doubt it would be worth the effort for them.

because right now there's no demand for it. if there was a period of zero/negative interest combined with low confidence in banks, I'm sure that non-fractional reserve banks would pop up. Either that or people stash their money overseas.

They already do this. That's how payment cards work.