And restructuring tends not be stay “gov owned” - the government assumes ownership to stabilize the market then tries to sell off the business to another business. Often there’s some incentive to assume a massive amount of customers and assets. The gov may even take on the intermediate loss (the FCID is an insurance agency after all).
Yeah, I can see why in general the government wouldn't want to hold on to assets, but bonds are kind of a special class of asset in that they do eventually mature and will naturally just be something they don't need to manage (within a relatively short time period too). If you expect that the sell off could take years to complete, some of those bonds will be halfway to maturity by the time they're sold.
If I'm the FDIC and I have the opportunity to return 100% of the funds to depositors at the cost of just holding on to a bond for a few more years than I otherwise would, that seems like a tradeoff I'd make to stabilize a lot of companies. (I'm of course biased here)