MMT doesn't claim anything like that. MMT says that a government that have its own floating currency its not financially constrained (the key word here is financially). They also claim that the size of the public debt (but not the deficit!) of such a government it's irrelevant.
Governments (that spend its own floating currency) can't spend indefinitely in a period of time because they are constrained by the real capacity of economy of the country. If they spend beyond that capacity inflation happens. This is cannon in MMT, it's not a complicated idea, it's even in the most superficial introduction to MMT and it's beyond me why somebody, acting in good faith, would keep changing, what the MMT economists are saying.
Your hyperinflation comments have been answered elsewhere in this thread.
But yes, they seem to be preferring to talk past rather than engage with mainstream macroeconomists. The sheer rhetorical effort they devote to convincing their readers the money multiplier is the wrong foundation that underpins all modern macro and not a simple pedagogic device for explaining how leverage works and why deposit insurance became a thing....
If you have a model that have the components right but the causality going in total opposite direction, I think is kind of fair to criticize its pedagogic value.
The week after, students learn about money markets, credit and money demand as liquidity preference.
And MMTers aren't saying "the second week of undergrad teaching could be improved by refining this model", they're saying "mainstream economics is built on this foundation that only we are clever enough to know isn't true".
Props for the Pratchett quote though. Sounds like something Detritus would have said. :)
MMTer: Public debt can be monetized, inflation is created by spending (public or otherwise) not by more reserves, central banks can control the interest rate independently of the quantity of reserves in the system.
Anti-MMTer: Wait, if you add reserves to the system, banks can lend more! That's inflationary!
MMTer: Banks can lend always anyway if makes business sense. Their only limit is the capital requirements of every particular bank. If lending makes business sense, banks can find the legally required reserves, they are not constrained by reserves.
Anti-MMTer: But the Money Multiplier!
MMTer: Facepalm
I wish I could remember in what book was the Terry Pratchett quote. It's a great quote.
Literally every single central bank's policies are designed and implemented by mainstream macroeconomists, as were the capital requirements. "Banks can lend always anyway if it makes business sense" is the system mainstream macro built. Of course, mainstream economists also consider the "if it makes business sense" bit (and to a degree the "capital requirements" bit) matters, and have models observing that the flow of money actually injected into the economy at a given interest rate being finite and relatively predictable, and they can make it go up or down in different circumstances by changing that interest rate. They also (since the 80s, at least) have a sophisticated enough grasp of inflation to figure that how the dollars are injected into the economy matters rather a lot.
As I said, it's really hard to get MMT people to sit down and describe exactly what they are claiming, b/c they have to face up to these counterexamples. Like: "why couldn't Venezuela print money indefinitely to pay for what it wants?"
To which the MMT response is some version of: "Well, I didn't mean that!"
Well ok - WHAT did you mean? They are always slippery and evasive (at best) about what they do mean. They do not engage with conventional macroeconomists for the most part. And that's not because conventional macroeconomists don't try to engage with them! If it were possible to do what they propose, that would be amazing! You would have wide agreement on that within the profession.
I share many of their political goals - I'm on the left too. But I don't see how it is remotely possible to achieve the goals they propose in the manner they suggest.