It's a good metric for a tax base.
> unless you think an $8 Big Mac is twice as productive to the economy than a $4 Big Mac
Which is why we consider both nominal and real GDP. (In your example, the former represents 2x nominal GDP. They're equivalent in terms of real GDP.)
It literally straightforwardly is. It provides the same number of calories, to a worker who is twice as productive in the $8-per-big-Mac city as the $4-per-Big-Mac city. Differences in per-capita productivity between supercities and hinterlands are vast.