I think MMTs have to make up their mind on this. Either money-financed fiscal expansion increases total spending or it doesn't. Either there's a real resource constraint that eventually becomes binding as total spending increases or there isn't. Finally, ... 1/n https://twitter.com/SamHLevey/status/1322654139088834562
...either sovereign money means a government can always avoid default or it doesn't. My understanding of the MMT position is (1) that both money- and bond-financed increases in government spending contribute to aggregate spending, ceteris. paribus;...
(2) that increased spending will eventually cause prices to rise (there's a real resource constraint that will bind at some point); and (3) that a sovereign money issuer can always avoid default by virtue of its ability to create the money it needs to finance spending.
So, let's suppose a sovereign money issuer elects to take on a very large scale expenditure program. It pays for it by monetized debt issuance (interest rates are pegged). Spending increases. Eventually full employment is reached--the real resource constraint is binding.
If G continues to grow, it has two choices: allow P to rise, or allow interest rates to rise (monetary discipline). Note that it has to do either of these things IF it continues to expand its own expenditures. (It could stop, but suppose it rejects this "austerity" option.)
(As you suggest, from a consolidated balance-sheet p.o.v., there isn't a meaningfully-distinct "third option" of bond-financed borrowing. The meaningful choices from that perspective are the two already mentioned.)
So, the government can either "crowd out" private-sector spending (increased interest rate), or it can allow inflation. The second option is really the one that takes full advantage of its status as a sovereign money issuer.
Assuming it goes that route,although the nominal value of its "liabilities" continues to increase, their real value does not. Of course, the binding real resource constant means that this approach also withdraws from the private sector whatever real resources go into G.
If we allow for interest-earning debt then of course the inflation also reduces its real value. This will indeed not be so for Inflation indexed debt, which is in that sense analogous to foreign-currency debt--a departure from strict M sovereignty, ...
and hence limits the otherwise absolute ability to avoid default. Still, the point remains that inflation can serve as a means by which a gov't can avoid default when it faces a binding real resource constraint. Of course it is never called for otherwise.