In fact, the Burns / Volker shift in policy and its consequences is ample demonstration that the Federal Reserve has a lot of control over whether we have very high rates of inflation or not.
Agreed. So-called reserves are not what they used to be, nor is the Fed sticking to keeping only treasuries on their balance sheet.
The Fed's actions had secondary impact on the real estate bubble. Dramatic enough actions by the Fed would have changed the behavior of everyone participating in the real estate bubble. But the Fed didn't put guns to anybody's head, and force them to buy more house than they could afford, or to lend acres of money to deadbeats. Free men did that all on their own. Then, when it was hurting the real economy, the Fed *did* do its job, raised interest rates, and broke the real estate bubble.
In the glowing fallout aftermath, it is a little silly to pretend it is all their fault because they should have nuked New York City a year earlier.