Not because the Fed wants to, but because they have to. IMO, if they could, the Fed and government in general would endlessly try to kick the can and artificially stave off recessions. And they have, with multiple money printing binges since 2008. Every potential downturn gets addressed with trillions in QE. Nobody cares, and nobody would do anything to change that. But IMO, the one and only thing that would change it is the one we got - inflation. Inflation is a bigger societal problem and political problem than recession is, and the Fed and government finally found inflation with their 2020 QE and free money policies. Low, manageable inflation and QE can't co-exist at the same time, inflation can essentially tie the Fed's hands in regard to QE, because if inflation blows out, it is a massive problem for them. I think that's the only thing that will prevent them from doing it again, and the only thing that will keep them in check. The Fed thought they could almost do QE with impunity, but the inflation of the last few years proved them wrong.
I also think the Fed realizes that buying all those MBS was a huge mistake. They know they distorted the market and caused long lasting issues, but they blame it on "supply" completely ignoring the fact that the reason there isn't enough supply is because they generated massive demand by buying so much MBS and artificially repressing rates to under 3% on a 30 year mortgage.
They are now talking about the possibility of outright sales of MBS, because they are trickling off the balance sheet (surprise, surprise, with market rates at 7%) and they know they need to get them to zero. The Fed has been awful the last 15 years, and has clearly pushed policy that greatly benefits asset holders and punishes savers and non-asset holders, but it seems CPI and PCE inflation may have ended their playbook of constantly boosting asset prices and repressing rates.