"Well, even supporters of Modern Monetary Theory admit unlimited borrowing will almost certainly end in a serious inflationary problem if the economy were to achieve full employment."

Firstly, borrowing is "NOT" a funding mechanism for a sovereign currency issuing government with a fiat currency. Why would the one entity with infinite availability of US dollars ever need to "borrow" its own currency back to enable spending? Money is created when Congress passes legislation and the Fed simply acts as a clearing bank for Treasury payments to make sure its checks don't bounce.

Investors can exercise thrift and benefit from the interest payments Treasury bonds offer, but their choice to buy, or not buy, bonds isn't relevant to the government's ability to spend new money into existence. Ditto for tax revenue.

Yes, continued government spending past the point of full employment would be inflationary, which is why we shouldn't do it regardless of MMT or any other system utilized. MMT also recognizes that inflation is not entirely a matter of the money supply, but is largely a product of supply chain malfunctions making resources scarce. Often it is necessary to accept some inflation to assure the people's access to such scarce resources if they are critical to the society.

MMT does advocate for a federally funded guaranteed job program that would automate the economic impact of spending by increasing spending countercyclical to the business cycle. It would also serve as a floor for wages and benefits that employers would have to outbid to gain workers. They would, however, gain workers with their social and many job skills intact.