Personally I found the comparison interesting as a thought experiment, but I'm not sure I think "barter" is the best term or that suggesting PoS is more "money" is the best way of putting it.
PoW was an attempt to mirror gold mining for a specie money. Not just for barter or for mining as such.
If anything, (allegorically) PoS can be seen as more "fiat" than PoW.
In other words there is no "specie", in this case represented by virtual bitcoins mined in a costly way, supporting it.
This can have both negative and positive implications. But the difference between the two is still less than between state issued fiat and gold money / predetermined to be deflationary or less inflationary cryptocurrency.