> the most relevant example here is their model's assumption that governments can and do spend money into existence
There are three points here. First of all, they are very clear that this only applies to monetarily sovereign governments (i.e., not Euro members, not state governments).
Second is their claim that directly spending money into existence is the more natural way of looking at things, and everything involving debt issuance is a voluntary add-on. That's not how things developed historically, but it does make sense when you think about how you would design a state-run currency from first principles.
Third is their claim that, as a first order approximation, even when all sorts of debt issuance dances are in place, the economy behaves as if they weren't and government simply spent money into and taxed money out of existence. [1]
The second point is admittedly a bit philosophical and subjective. You might care more about the historical account than the first principles account.
However, the third point is quite objective, and if you have a concrete example of how debt issuance actually makes a significant macro-economic difference that contradicts MMT, I would be highly interested (and I assume MMT economists would be as well).
[1] One way to look at it is this: Debt issuance is a red herring; what matters is the central bank policy of (usually) maintaining a positive interest rate. Debt issuance is only a way of shifting the cost of this policy from the central bank's books into the general government budget, i.e. it is a political that hides the true cost of monetary policy so that the public won't be as outraged about it.