I think something like this could make large banks more of an asset for the economy rather than a liability. I wouldn't want to just set a maximum size. If a bank wants to get huge and maintain conservative and safe asset/deposit ratios, good for them.
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.
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.