Must you have an uncompleted destination card in Ticket to Ride?
Drawing Destination cards later in the game is optional - the only time you have to draw Destination cards is at the start of the game.

If you finish all of yours early enough then it may be worth drawing more, but if you finish them later in the game it would be unproductive to draw more, and your efforts are better spent trying to block other players.

Since Destination cards are always kept secret from other players until scoring, any rule that did say you had to have incomplete Destination cards would be based entirely on trust.