by "weakness", I mean the kind of total loss of trust in the market that prevents the entity from working. And you are right that this should apply only to banks that are systematically important, but when you look at Europe, the large majority of banks are systemically important to their home market, given that they are often active in other countries as well and thus their balance sheet is bigger.

And nationalisation need not mean subsidizing one - see the example of Fortis, where the governments have taken over and sold off various bits quite quickly, without a loss to them

In the long run, we're all dead. John Maynard Keynes