Lots of people in the UK watch iPlayer without paying. You only need a TV licence to watch live broadcasts. If you stick to recorded programmes on iPlayer it's perfectly okay to use it without a license.
You mention fairness... Currently people in Europe have no ability to pay for most BBC content even if they wanted to. Chances are it wouldn't stream very well to them anyway, due to all the servers being located in the UK. If they get it for free it doesn't take anything away from the people who have to pay.
The only real issue I can see is the extra server load, and thus cost, that it would generate. That could be offset easily using BitTorrent. Just make .torrent versions available. BitTorrent Inc. have streaming technology. ISPs who want to cache can put seed boxes inside their networks like the currently do with caching servers. Okay, there is no DRM, but it sounds like that needs to go away anyway unless they want to keep trying to limit iPlayer to just the EU.