Private credit is not supposed to be systemically important and it's not supposed to need bailing out. Maybe we'll find out how true that is in practice.
We can check if governments went back to their own tricks or not after 2008. What were the interest rates after 2008? Quick check ... yep, they went back to the old tricks.
When "shit hits the fan". Either governments really cut spending, leave pensioners without income and see their new loan interest spike to 10%+ (if they're lucky) ...
OR they do a massive cash injection saving the banks, and increase spending.
Which would you chose? It doesn't even matter. If you were the government and chose the first option, you would quickly find suddenly everyone across the political spectrum uniting to depose you. A decent chunk of people would literally not have any other choice but to do that.
(of course, as per usual governments aren't behaving "correctly" according to economic theory. If you take the old "government as spender of last resort" governments should have radically cut spending in the last 10 years, because there was no need for extra spending. If you take the new "government invests pensions", then of course government spending needs to be investment. In other words, governments only allowed to spend like a normal investor, expecting and demanding a return. Ie. no social spending increases. In practice governments increased spending at any cost, and so we're in trouble again)
Oh and should I mention that for any other entity investing pension money in loans to yourself is a very unique thing in law. It is THE ONLY financial crime where corporate structures do not protect management. You're the worldwide president of ExxonMobil? Doesn't matter. You do with employee pension money what government does with it? (ie. loan it to yourself, in this case ExxonMobil). You go to jail. Directly and long-term. In America. In Spain. In Japan. In fucking Vatican city.
US government direct investment exposure is not likely to motivate a bailout in my view. The government might be motivated to bail people out for other reasons but not because they've lent too much.