The thing is, the central idea isn't actually as flawed as it's being made out to be - there's a reason that the Euros have been split between countries more and more (Poland/Ukraine, Switzerland/Austria, Holland/Belgium), and it's because it's an event that costs World Cup money, but doesn't have World Cup revenue to justify the outlay. Portugal were well and truly stung for the 2004 tournament, to the point there's a stadium in Faro that has 30,000 capacity yet will never fill it because Faro and Farense are in the second and third divisions respectively, so all it does is leech the local economy to stay open to not be filled. Something similar will be in Stratford very soon.
Another thing against the Euros is there's less casual fans going to games played by non-host nations, be it the embarrassing attendances for Euro '96 that didn't feature England or Scotland, whilst many nations have differing sizes of travelling support: Italy have a large home support but the further from Italy they play the less of them travel, whilst Greek and Portuguese fans can barely afford travel given how financially crippled their countries are these days.
Of course, it depends how many cities are chosen. The most ridiculous notion would be one team playing their group games in Lisbon, St Petersburg and Athens, a more logical notion would be playing their group games in Copenhagen, Stockholm and Oslo.