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You have that backwards. The market sets the long end of the curve via supply and demand,the Fed controls the short end of the curve (federal funds rate)

If the Fed hiked the (short-term) FFR, long term inflation expectations would go down, along with the yield of long duration Treasury bonds.

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You are largely correct for the pre QE years. But with QE, bonds further out the curve have been purchased by the Fed, and the yields for such maturities have been artificially suppressed. Warsh, at on time, really cared about this mispricing of risk. We'll see how he feels now that he's got his hand on the rudder and the orange colored man breathing down his neck.

There has been a distinct lack of QE the past few years, here is the Fed’s balance sheet charted: https://www.macrotrends.net/3003/fed-balance-sheet

They still own 7X the amount bonds they did pre-GFC, and 75% of what they did at the peak. In short, I posit it still has a massive effect on the yield curve and all assets (US and globally).

Long-term bonds can be replaced with short-term bonds which are constantly rolled over. It wouldn't make sense if the market was pricing in anything else than future interest rates.

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