> QE means buying assets that are not Treasuries.
The short answer is that it depends - it is not not QE. it depends on the magnitude. Current operations seem to go deeper into QE than regular OMO.
> The price of a bond, mathematically, moves inversely with its yield.
Yes? But the central bank han many other ways to influence the rate, eg. overnight rate and OMO instead of buying MBS, etc.
As you indicate yourself, having the FED as a market participant will artificially lower the yield on MBS, which is a form of planned economy on the housing market.
> You can't reduce the balance sheet and lower rates.
Why the insane focus on lowering the rate? Keeping rates below 0 in real terms for long terms can arguable have very adverse effects - especially the day the currency is not backed by the largest military in the world (Which, surprise, is not decades into the future anymore).
Regardless, the future will show what happens. We can nothing but speculate.
I don't think you understand bonds. The rates don't float once issued. They discount the price in order to sell at a certain yield at time of issue. After that, the prices float in the market based on current rates, but it's not a very liquid market. I own bonds with like 2.5% coupon and nobody will buy them and the estimated price is just that, an estimate, because nobody will actually buy them. I can hold to maturity and be made whole. I just missed out on buying higher rate bonds for the duration. It's fine.
I honestly don't know what the Fed does or how it does it. I think if you dig deep enough, it's like that Rick & Morty episode where Rick brings down the entire Galactic Bug Empire by changing a "1" to a "0" in their computer system, thereby making their entire currency immediately worthless.
Monetary systems work on trust until they don't. Then there is a world war.