I think you are swinging at the wrong ball. There are two questions: (i) will the expenditure be the best likely use of the resources consumed? and (ii) will the expenditure raise the costs of what it is spent on, including the multiplier spending?

1. A bridge is a good expenditure if the materials and labor add more value than they would have added if the expenditure had not been made. That depends on what the private sector would have done with those resources, if anything. That’s why recessions are a good time for government to spend.
2. But if the government building a bridge raises the cost of steel for cars, because we’re out of steel, we have to decide whether we want bridges or cars to ride over it. The relevant metric is inflation. If government spending causes inflation, the only value it adds is the bridge, which is “paid for” by the reduced purchasing power (due to inflation) of everyone who does not get paid to build the bridge or by the bridge-builder for something else. The $1billion doesn’t disappear into the economy; it competes for goods and services, to the detriment of everyone who doesn’t get a piece of it. That’s why boom times are not a good time for government spending.

Neither of these questions asks whether the economy “grows” by some amount on account of the bridge being built. If you were to go down that road, you would need to think like M. Bastiat, inquiring into the lost production that would have occurred if the resources used to build the bridge were diverted from some other productive activity. You would end up in the same place as I do, and as MMT does: if the bridge (and the follow-on spending) tap excess capacity, there will be no inflation, and the economy will have grown by reason of the bridge being built. But if there is no excess capacity, the bridge will crowd out some other spending, and any growth will arise solely from the bridge in fact being a more valuable use of the resources employed than would otherwise have been the case.

The relevance of MMT to today’s globalized, automated economy is that excess supply is upon us like water on the sorcerer’s apprentice. We are reliving 1896, when the technology of supply advanced faster than the technology of demand. MMT is basically the bimetallism of the 21st century, a way to put more money into the economy at a time when the producers need there to be more money in the economy.

All consumption, including government spending, is “paid for” by increased production or by inflation in the price of maximum production. A bridge “pays for itself” if it doesn’t cause inflation. No other test is necessary.