You do need a common measurement to be able to aggregate items together (a tractor and a sandwich, for example), and we generally use dollars for that, but I wouldn’t call that recursive.
You could also measure it in labor time, percentage of life people need to spend working, sea shells, or a variety of other measures depending on your aim.
if its the latter its somewhat disingenuous to use that word with its broader connotation instead of just 'sale amount'
One reply to that is to use different methodologies
The canonical reply is probably something on the order of “people can’t sustainably engage in practices where they exchange $1 of value for $0.50 of value, as they still need to exchange labor for food and other real goods.”
You normally see the latter play out through credit crises, where the benefits of some activity fail to materialize and therefore loans can’t be repaid, and a lot of pain follows.
Under that view instantaneous measures of GDP don’t mean much, but measurements averaged over longer periods, credit crises, etc. take on some meaning.
but we can assume that over time, and more importantly over many transactions, the 'true' value will surface (wash out all the weird signal).