Good idea.
When one clicks an arena, it should show you the current country numbers and prompt you to choose a side. Somehow, I think this would actually make it easier for people to change/switch sides, instead of logging on, saying howdy to all your friends, and then having to part with them again.
Perhaps an incentive system might also help. The dynamic perk system works as it is now, but when certain numbers advantage have been gained by a country, the country with smallest numbers would get a mega-perk boost, something like five times the normal amount, whereas the country with the largest numbers would get five times less.
My two cents.