What would motivate a large bank to buy the debt of a smaller one? They might buy up the assets (brick and mortar buildings, etc), and certainly that might be used to pay back the remaining outstanding debts, but the out of business bank will not be "merged," it will sell off whatever it can, and then fade into history.
The customer base. The surviving bank will acquire all the failed bank's customers. The customers aren't going anywhere. They're still going to need somewhere to put their gold, btc, grain, whatever the reserves are.
So, the successful banks should not be rewarded for their wise policies in not putting out too many notes?
And let's assume that that's exactly what happens: All the other banks suffer runs because they were stupid, and their assets are picked up by one big bank - or a cartel - that does a lot of business. Without the government to influence, what harm can they do?
But in reality right now, there is a government.
Yes, but you postulated a free market system.

Tell me, how exactly would a huge bank harm the public?