You’re describing as profitable lending by an entity funding itself by issuing Treasuries and then ignoring the cost of the interest paid on those Treasuries when deciding if the use of the money was profitable.
Inflation is not a direct cost of interest. If we are going to included opportunity costs in the definition of profit and loss, then we should include the opportunity cost of tax revenue plummeting if the financial system collapsed.
It’s not inflation. It’s literal money paid out via the government paying interest on its debt obligations (which were higher as a result of the bailout money than they otherwise would have been).
I agree that they should have done what they did. I do not agree that it was net profitable.