I would argue no. The issue is that the FDIC has deposit insurance limits already. The depositors are free-rolling on the amount they are getting made whole on above the limit. Then you are just encouraging some new kind of "bank" with limited access to become a customer (e.g. > $50M deposit) and then you can just put all "shareholders" in the role as customers. You are still giving free upside outside the rules that all other depositors are stuck with. Every investment comes with the statement: "Investment contains risk". If the bank wasn't leveraging these deposit as investment cash, there would have been no collapse.

You're right this produces risk but you're wrong about exactly how.

Any bank call pull in deposit and use them as capital. But being a customer also doesn't give one any particular upside - you just get interest on the money you deposit. And if you have a special bank with only large deposits and paying extra high interest, then regulators look at you and quite likely see something not to be protected in the same way.

The way you get risk is basically the way SVB did it. Share holders can lose at most their entire capital but they can get to play with all the money the depositors give them. If they bet on something that pays off big, they get that payoff minus the modest interest they pay depositors and if they lose, they lose at most their capital.

If you can use just a bit of capital to borrow a whole lot of capital, with the only risk to you being your original capital, then you can engage in very risky ventures, getting a huge payoff if you succeed and at worst losing your original capital if you lose.

Come to think of it, that seems a bit like what SVB did. Buying long term bonds when interest rates were likely rise seems like a recipe for disaster - and in fact the logical outcome was this bankruptcy. But there was a chance that interest rates wouldn't have risen, at which point the shareholder get a big payoff, pocket it and go on to the next risky maneuver.