This suggestion came up like a dozen times in different variations and I always loved it. Unfortunately I think this is one of several good suggestions we will never see implemented in this game.
Smaller nations would grow their talent pool without hurting the big nations. Losing a good prospect (team going bot, stubborn/dumb owner) can be devastating for a small nation, so allowing to switch nationalities could help a lot in this regard, as small nations could compensate these losses pretty easily.
Größter Knecht aller Zeiten aka His Excellency aka President for Life aka Field Marshal Al Hadji aka Lord of All the Beasts of the Earth and Fishes of the Seas aka aka Conqueror of the Buzzerbeater Empire in Europe in General and Austria in Particular