Of course technological progress will slow down if no fiat money injected, but nevertheless won't completely stop. Moreover, without fiat money any government in the developed world will collapse within months, turning quality of the life to medieval level.
It surprises me to read such praise of fiat money on this board. The 19th century largely got along without fiat money, particularly in the US and Germany went pretty much with metals. That posed a problem for banks because companies developed a tendency to invest from revenue, not from loans.
I believe the problem discussed here would largely go away if we'd use money that isn't someone else's liability. So far, the reason for unemployment is not AI (though that may change), it's the huge cost of using money. Our tax load is actually somewhere between 75% and 90% because of inflation and interest. It is hard to be profitable if you can keep less 20% of your income.