I would think that when the European championships started, 99.9% of FT shooters were British, so it made sense to hold the championships in the UK.
As FT has spread, the justification for holding the event somewhere else in Europe grows.
However, even now, I would guesstimate that the Euros attract 80-90% of Europe's top FT shooters and, as Steve has said, many thousands of pounds of sponsorship/income.
If you can guarantee the same level of sponsorship, competition, and organisation, then I'm sure we'd all be happy to see the Euros held in another country.
And, by the way, as its a championship, and open to all Europeans, why should it be called something else?