Fed Independence

Who cares about the nominal, not real cost of borrowing? If you mean inflation, it is not clear that the Fed always wants less inflation than congress or president. If you mean real costs, the Fed must have limited power to lower real rates for very long without repression

Governments without independent central banks and with large nominal debts have taken monetary policies that increase inflation. The market will anticipate this and price in more inflation.

I agree it would increase the cost of borrowing but it is not obvious it would "substantially" increase the cost of borrowing. Currently, there is no credible competitor to the dollar as reserve currency - even with a less independent central bank.

The timing of when it happens will be hard to tell, but the list of countries where this is happened shows that the direction of travel is certain.
-see background information here

Fed independence is key to controlling inflation, and without that important factor, investors---particularly foreign investors---will place less faith in U.S. debt maintaining its value, and will therefore charge higher yields.

Evidence suggests that greater central bank independence lowers interest rates on sovereign debt. The balance of democratic accountability and independence, struck by the structure of the Fed has lead to low and anchored inflation expectations and low US interest rates.

Uncertain because if the President succeeds in inducing the Fed to lower interest rates (as Nixon with Arthur Burns in the 1970s), nominal borrowing costs go down in the ST but as inflation expectations increase in the LT, the government faces higher overall LT borrowing cost.
-see background information here
-see background information here

Given the dire fiscal situation of the U.S., loss of independence would lead to financial repression with monetary policy put in service of the fiscal situation.
-see background information here

In a regime of fiscal dominance, inflation expectations will rise when the government's fiscal position deteriorates, driving bond returns down in bad times and therefore raising the risk premium demanded by investors.

By "risk premia" do you mean inflation premiums or default premiums? Both might rise. Don't rule out bondholder haircuts in a crisis.

Uncertainty about how much inflation will be caused by future governments will choose in bad versus good times could increase their real interest rates. Government bonds in the past have offered low returns to investors because they are very safe. This may disappear.

I agree the risk premium will increase. It is not obvious it would "substantially" increase. A less independent central bank will cause some to diversify their U.S. holdings. De-dollarization is impt. China has established 31 bilateral swap lines consistent with de-dollarization.

See above, same argument and evidence

Same reason as above.

The dominating effect probably would be a rise in inflation risk premia.

Evidence suggests that greater central bank independence lowers interest rates on sovereign debt. Less independent central banks are more inclined to inflate away fiscal problems and so raise inflation risk premia.

Investors would demand higher compensation for the increased risks they perceive from reduced Fed independence, such as greater inflation risk or concerns about monetary policy being influenced by political rather than economic considerations. Probably they are already doing that

there would be substantial policy uncertainty that would raise the risk premium on long-term debt.