The Fed is only part of the reason, we have a structural issue with how the S&P is calculated using a Market Capitalization formula.
A lot of new money comes in via 401K contributions, etc., and a lot of that is going to Index funds, mostly the S&P 500 since it is always included in retirement plan choices. Apple, Alphabet, Amazon, Microsoft and a few others are about 20% of the Index and money automatically gets allocated to those stocks via the Index providers, continuing to push up the most ludicrous valuations.
Those four stocks ALONE are over $7 TRILLION in Market Cap. The Fed mostly owns fixed income and mortgages so they have less influence on the stock market.
That is true only because other investors who are not index funds also want to own those stocks. Nobody wants dogs like IBM and GE.
Moreover, if the S&P went down significantly, it is entirely possible that all the 401K investors who swore they’d stay in the S&P until they’re 70 would start to sell some of their holdings anyway. Such selling would easily offset new money, and would accelerate the downturn. The index funds would have to dump huge amounts of Apple, Facebook, Google, Microsoft and Tesla.