Something I don't understand: The people withdrawing above FDIC insurance limits aren't just putting the millions they withdraw under a mattress. They have to put it somewhere. And the most logical place to put it seems to be one of these big banks. Don't these big banks stand to gain from the collapse of small banks, as people flee small banks and into big banks? What risk do the big banks have of experiencing a run? Where would people put all that money?

Game Theory. Will you be the last one standing?

Also, I imagine the "people flee[ing] small banks ... into big banks" makes this particular stabilizing action easier. The big banks just redirect all the new deposits they're getting back to the small banks where they came from to stabilize things.

There are bigger considerations here for these banks than the gains they would make from the failure of small banks. They know that they are in a very nice position with the government guaranteeing all of their debt while at the same time leaving them free to make as much profit as they can. They know that the mass failure of regional banks while big banks gain would be a political event as much as a financial one. They know that they are some of the most widely hated organizations in the US, and that the political fallout from such an event would not go in their favor like last time, so they will pull out all the stops to prevent it from happening.

Every bank failure sends the stock value of all banks downwards. As well as corroding political confidence in the system.

Take a look at what happened with SVB failed and needed to raise the cash to meet their deposits. It massively depressed the value of a lot of the investments they held in the markets. As other banks fail, similar kinds of movements can happen and potentially have other downstream effects causing a lot of instability and chaos into markets. Maybe the big banks will be able to capitalize on those, maybe they'll end up hurt as well. Keeping the market healthy can be a good thing.