It will never happen, but just authorise the FAA IR for use in any ICAO Country
It is up to each
State of aircraft registry what privileges a foreign license or rating gives on an aircraft of that registry.
What you are asking is for say Germany to accept any ICAO IR (just the FAA one would appear discriminary) for a D-reg, for all airspace class.
This would be totally logical but is politically impossible. It would fly in the face of European protectionism (which goes back decades but is why e.g. JAA was set up in the first place) and a raft of elitist attitudes. It will never happen. In JAA-land, only one (rather far away) country ever accepted an ICAO IR in that way and they stopped it a few years ago. The CAA accepts it which also exceptional but only OCAS which is useless.
The politically possible outcomes are
- a European private IR, gradually hacked together under political pressure to reduce the foreign reg scene, and probably together with an attack on the latter scene, to make it "stick".
- a status quo (a climbdown)
The 2nd one is politically the easiest, because nobody actually loses anything except face, and one can always blame that on somebody else. Nobody would gain anything from attacking the foreign reg scene, either. Politicians have to think short-term and what credits they can earn by doing something.