Taxpayers don’t need to bail out the Fed. The Fed literally creates money ex nihilo.
that's too simplistic. the fed has wide latitude (probably too wide), but it should correlate with the (fuzzy, hard to accurately measure/model) productive capacity/velocity of the (globalized) economy, not just an unlimited well only constrained by inflation's devaluatory noose.
moreover, considering our technological progress and trajectory, i'd love to see us revisit the idea that money can only be injected into institutions (via central banks), which was a limitation of scope imposed by the practicalities of pre-21st century life. it's also a gatekeeper's gold mine on a no longer necessary choke point. we should move towards injecting money straight into the hands that create value, not into those of middlemen like bankers.
But from a practical, tangible, rubber-meets-the-road, this-is-how-they-do-it point of view when the Fed buys something, it pays for it by writing a new number in my Fed account. That new number is money.
So any time the fed takes on a debt made by a business at anything other than a discount the fed is bailing out bad business decisions, and that means the taxpayer is paying for it.
If the fed just “prints money” to cover those debts the real value of the USD collapses, and that hurts individual taxpayers more than the big businesses being bailed out.