Your mistake is misunderstanding the power central banks have in managing these assets. The Fed can make the yield whatever it wants. The Fed potentially has reasons to let the yield be high but it's a choice.
> The Fed can distort the market by buying treasures themselves
What you call "distorting the market" the Fed would call something like "setting the parameters of the market".
Regardless if you're ideologically opposed to the Fed actively managing the market for treasuries. The fact is that they can, and they do.
> inflation and reduces credibility
So you admit that the Fed has this power but they just choose not to exercise it? In any case, the Treasury's actions "fuels inflation" every bit as much as any intervention the Fed might take in the bond market.