And that issue is non-starter, for the same reasons given in the podcast you even linked:
> GDP is just GDP. It's just like, how big is the economy? It's not that hard. And you can't take the government part out of it because the government is a significant part of that.
(Note that I agree with your larger point)
One discussion of this point can be found in an Indicator podcast[0] from a couple of months ago.
[0] https://www.npr.org/transcripts/1237470062