Does the result of the last game of Euchre determine who gets to deal first in the next game?
I would have to agree with you. A previous game definitely has nothing to do with the proceeding game. It is equivalent to playing a game then a few years later the winner is still able to be the dealer without the blackjack deal (well maybe not quite that far, but you get the point). But just clarifying we are talking about entirely new games, not rounds? If we are talking about games then yes redo the blackjack deal.