Second, it makes no difference whether the government "must" borrow. What matters is that the government does borrow, and it pays market rates.

The Fed, sharing a balance sheet with Treasury, is "always" the gorilla in the room when it comes to setting rates. It can simply take on any deficit, at its desired rate, that Treasury needs and it will balance out at the bottom line. This is the core of our monetary policy. The games bond investors play between issuing and maturity have no bearing on anything as they are always zero-sum.

If the Fed suppresses those rates by monetizing the debt, that just puts more inflationary money out into the economy chasing goods that aren't there.

The debt was originally bank reserves which just sit in accounts earning nothing. The debt "is" a process that injects money into the economy when bonds mature, so monetizing is not a valid term in conjunction with either. Any interest the Fed accrues is returned to Treasury via the shared balance sheet.

the government is in effect crowding out private demand for goods by outbidding the consumer for loan funds.

Existing deposits are not used to loan. Banks create deposits/reserves when they issue loan contracts. Those reserves come at a cost to lenders to facilitate interbank transfers and will be retired as principle is paid down. That cost is set by the Fed as the overnight rate. Paying off a bank loan reduces the money supply.

The government can spend too much money, and a budgetary constraint, artificial as it may be, may prevent that from happening.

Spending too much can happen regardless of the amount of money in circulation. If the resources the money is intended to deploy are not sufficient to absorb the spending the "price" of those resources may increase as a result. That will not transfer to other goods or commodities, so is not really "inflation" unless the desired commodity is universal in the economy, such as energy/oil was in the '70s.

Even then, the government can become the intermediate "distributor" of the commodity and absorb any losses at Treasury without inflicting them onto the private sector. This, however, is far too close to "socialism" for Americans to ever accept in today's political environment.