They are, in isolation. The _problem_ is that PE doesn't generally trade assets in public, which means that valuation only really come when you're either wanting to buy, wanting to sell, wanting to re-loan or in deep shit.
This means that something like MFS can happen (https://www.reuters.com/business/finance/mfs-creditors-claim...) where assets appear to be used to raise two different loans without the other lender knowing.
But! banking can absorb a few billion right? yes, so long as people are not asking questions about other assets.
Because PE assets are not publicly traded (hence private in private equity) the value of assets are calculated at much lower rates than on a public market. This means that the assets that PE holds could be wildly over or under valued. The way we assess the value of PE holdings is thier looking at the Net Asset Value calculations (which might be done twice a year) or infer the value based on public information.
Now we are told that markets are rational and great at working the value of things. This dear reader is bollocks. Because PE is a black box, if a class of asset that they hold (ie SaaS buisnesses, or high street stores, or coffee trading etc) looks like its not doing well, people will start to write down the value of people holding loans given to PE, or shares in PE.
This creates contagion, because one PE company is in distress, the market goes "oh shit, the whole thing is on fire" and you get bank runs (because where is the money coming from to loan to PE? thats right banks, eventually)