Under the ICAO agreement, all member states must accept PPL privileges from 'foreign' licences.
which has been ignored by every country I know of except the UK
The best you get is the U.S. piggyback license regime where you turn up in person somewhere and they give you one. Around Europe, validation is available but the conditions vary; one seemingly popular version is that it is vailable only to non EU residents (France AIUI).
would you rent your SEP to a JAA CPL/ME and allow them to use ICAO privileges to fly it?
I used to rent out my TB20 so let me answer on that basis...
YES. UK ANO Article 26 automatically validates ICAO licenses for a G-reg plane, for VFR flight worldwide.
For me, a far bigger factor was whether the renter was qualified on type and/or had the right attitude to learn the procedures. But that is another story.