This would be totally logical but is politically impossible.
I'm not sure that it would be impossible, and Euroland could do it without losing "face"......
For example if limited to "private privileges only" - which is what the FAA would do to a Euro licence holder - then it needn't impact on "Commercial" aviation in Euroland, which after is is where 99% of the current IR's come from. If the rules then stated that the Foreign IR holder then had to renew their Euro IR (based on) the same way as normal IR holders then in fact it'd actually generate European business.
For one to fly commercially in Euroland, one would still need to do the Euro IR.