The problem with that general idea is that nontradables are also immune from international competition. Tyler Cowen calls this the “low accountability sector”, while Arnold Kling calls it the “new commanding heights” of the economy.
I do have a major quibble with this though. It seems to me that the whole point of being in the tradables sector is to eliminate jobs through efficiency. Thus, the gross number of jobs created in the tradables sector might be huge, but they are constantly being churned in favor of new and different jobs. So, I’m not sure that this Schumpeterian sector is as underrepresented as it first appears.