If the bank isn't insured, then depositors end up taking losses, which means that - certainly for people with less than $250k of deposits - this "safe" bank is strictly less safe than a traditional bank. (And realistically, almost certainly less safe for large depsositors too.) So why would you pay money for a strictly inferior experience as a depositor when a traditional bank would pay you?
And if the bank is insured, then you've got to cover the insurance fees out of the fees you collect from depositors. And the insurance is presumably either FDIC, or something which is some mixture or less generous and/or more risky (FDIC is backstopped by the US government; Joe's Discount Deposit Insurance Agency...isn't.). But even in the best case it's FDIC, in which case...what's the point? You're exactly as safe as a traditional bank, except you're refusing to make loans, so you have to charge your depositors fees.
> If this model were competing with traditional 10% margin banks, it might well be supported by stockholders due to its ability to withstand runs a priori.
It is true that while these models have no benefit to depositors, they nominally benefit shareholders, we are going to be wiped out in fewer cases. (Note, though, that a bank with this model can't neccessarilly withstand runs. Let's say a false rumour sweeps through that one of these banks has had money stolen from the vaults. People correctly realise that if this is true, and they're the last ones to withdraw money, there will be nothing left for them, so the race to withdraw first. Unlike a traditional bank, in this case all the deposits can be returned, but now you've got a bank with branches and staff but no depositors and thus no revenue. And the panicked depositors who pulled their money out and put it in some other bank will have no incentive to bring it back now that you've proven you could cover the deposits. Bankruptcy is likely inevitable at this point.)
But in any case, sure, given the same risk adjusted return, it's rational to always prefer equity in something like Custodia than a traditional bank! But since there's no benefit to depositors, there's no way a bank could make an equivalent return. And while plenty of investors do want low risk, low return investments, it's hard to imagine any of them taking a flyer on something like Custodia, which is likely to be the exact opposite of that.
None of this actually works.