I am not convinced for the reasons given.
I see no reason why the private IR couldn't be an ICAO license - after all the FA IR is ICAO compliant without the bloated theory content.
Moreover as I said earlier the PPL is ICAO compliant BUT is a private license without commercial privileges.
If airports want to exclude private flights they will do so anyway - either using pricing or as we are seeing in Belgium - other means. Realistically how many private light singles or twins go into Gatwick at the moment and for how long has this been the case?
No, I don't think yours is a reason for not developing a private rating, but, as I said earlier, this is all dream world, its not about to happen so what I think is irrelevant in the big scheme of things.