However, they were afraid this solution to a current problem would be seen as a move to privatize warfare: as in in privateers! That's the etymology.
Some less rational factions will undoubtedly hail this as a crazy right-winged conspiracy to privatize the military. But Founders did not design a Constitution with powers that undermine other powers. If letters of marque were a tool of privatization, what good would it have been to include provisions, just a few lines below this, “to raise and support armies” and to “provide and maintain a Navy”?
And exactly what would be wrong with that? It wasn't as if the constitution provided for a standing army. However, in order to give people the opportunity to take advantage of a letter of marque, we would also need to repeal the Neutrality Act. Is anyone prepared to do that?