Question: Why does the Fed need to keep purchasing US government debt and mortgage backed securities if there is sufficient market demand for these assets?

I contend that the obvious answer is that there is not. Some would tend to disagree.

The Fed balance sheet is the largest it has ever been as of yesterday. 7.9 trillion roughly
US government debt represents 5.1 trillion and Mortgage backed securities about 2.3 trillion.

The US trade deficit is at record levels so this should provide lots of foreign demand
US corporations re making record levels of dough so no potential shortage there.
US interest rates are higher than many foreign countries, hence rate differential might attract money, so potential there

The simple fact is that US treasuries are simply not attractive for a variety of reasons, (primary one being quantity needed) and if they want to be able to support the governments
fiscal policies, ( the people that appointed them) then they need to keep rates low enough so that the large deficits can be financed now and into the future.

The Mortgage backed securities are similar, what fool would want to purchase 30 year locked in commitments at these rates.

The only thing making the Fed not have to buy almost all of these assets is that most other central banks are doing likewise. ( keeps the US currency from plummeting )