Should the government peg the S&P 500?

The very well known macroeconomist Roger Farmer says yes:

It is time for a greatly increased role for monetary policy through
direct intervention of central banks in world stock markets to prevent
bubbles and crashes. Central banks control interest rates by buying and
selling securities on the open market.

A logical extension of this idea is to pick an indexed basket of
securities: one candidate in the US might be the S&P 500, and to
control its price by buying and selling blocks of shares on the open
market.

That is from the FT.  Though he says he is warming to the idea, to my ear Mark Thoma sounds skeptical as am I.  Public choice considerations aside, if the Dow is valued at 7000 in market opinion and the Treasury (Fed?) is propping it up at 8500, a lot of people will sell shares into the hands of the government.  How much are the shares worth then?  How hard will the government try to break the shorts who speculate on lower prices?  Will this work any better than currency pegs?  What are the implications for pursuing other monetary targets, such as the rate of inflation?  If the peg succeeds who would hold other, riskier assets?

Some people might even say that the "Greenspan put" was part of what got us into this hole in the first place.

Farmer is working on a book How the Economy Works and How to Fix it When it Doesn’t.