Your ideas about central banks are seriously outdated. Their role has diminished as markets have grown gigantically. Central banks only deal with puny amounts compared to the global markets.
But according to you, the puny amounts that the Fed transacts scare markets that have vastly larger amounts into fulfilling the goals of the Fed. I'm not persuaded.
The facts show the Fed has failed repeatedly, year after year to reach its inflation target. Likewise, the Bank of Japan has failed for the better part of a generation.
The facts show that the Fed's multiple QEs have failed to lift the economy anywhere near 3% growth.
The Fed isn't the god you think it is. But I understand that conspiracy theorists always nitpick anything that contradicts them.
From the central banks' point of view, more inflation and growth today would be nice, but the crucial thing is to maintain what remains of the global asset bubble after the bust of 2008. In this they have succeeded by a combination of announcing boldly but treading carefully and creating just not enough pain to be politically problematic (even if they would never call it a bubble, of course.)
You're right that their power is not unlimited, especially at a time like this, so they have to accept some degree of failure. But the system is basically holding, so far.
But trust me, if the bottom falls out of the system tomorrow, they will still have ultimate control. They will just have to eat a bit more humble pie, effectively devalue currency against gold, and get their stability back. In fact, stability will come back big. (Most likely, the program will be called 'helicopter money' by what it looks like on the surface.)
WRT to market vs. central bank power -- say you have $10K invested in Treasuries, and know that the US government, in the end, can't remotely repay its debt with anything near the purchasing power of what creditors lent it, and you know that every other investor knows it. What can you really do? Sell Treasuries and get 0% in a bank account? Let's say a bunch of investors all decide to get out (say, after a political episode on Capitol Hill,) they all know that the Fed will step in to buy Treasuries if the price falls too much, and they can easily end up losing on the trade. So they and you decide to put off the decision for another day, especially since the market is still perceived to be liquid. Since everyone knows most others will do this, the price of Treasuries stays at its over-valued level, and the Fed hasn't spent a penny.
Now for a major holder of Treasuries like China or Saudi Arabia, it's a slightly different bargain. You are much better off playing ball with Uncle Sam, hold the Treasuries, and get what you can from Washington policies. Ultimately, you can't win an outright confrontation, since you know you're a corrupt dictatorship and your people tolerate you only barely (the 'free' Western media has made sure of that) and you need US co-operation, in one way or another. (Especially since you know the only damage you can threaten Washington with is that the Fed will swallow some more pride and print money to buy up your Treasuries.)
This is a microcosm -- the entire system works this way, globally. It's the essence of using state power to support an asset bubble. For the public, on the receiving end of this power, the choice is always, ultimately, lose-lose.