I even think the US did that in the 80ies, with the savings and loans crash. But I know less about that.

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Bankruptcy means unable to pay one's bills, and writing down loans (assets) in most cases also means writing down liabilities (the loans banks themselves take out from others to leverage their own capital while making loans to others).  So profitability would be reduced and in many cases losses would also be experienced by shareholders of banks, but bankruptcy would only occur in some cases.  Even in those cases, however, as the US TARP program showed, it is both easy and relatively costless to prevent those banks from failing if they are deemed too large to be allowed to do so.  Central banks, as lenders of last resort, can just print money, for free, and lend it to banks for the purpose of just keeping capital high enough on balance sheets to stay in business while the bank raises its own capital through retained earnings and other investments.  As long as the money isn't lent, it cannot produce inflation, so it is essentially just a waiver from the government which allows banks to continue operating outside of normal regulatory or best practice standards.

Why do things seem to work differently for banks than for other businesses? Because banks aren't in the business of making any real things, just arranging social commitments between people.  They are in the same business that government is -- organizing people to do things in common projects.  Just like in government, it really doesn't matter if banks run profits or deficits if their stakeholders are willing to let it pass -- willing to let some of their own commitments be relaxed and worked out later.