If you ask all Spurs players especially English, I think you will be surprised,,, most will say they want to win the title in England more than UCL. Proof that you are better than 19 other teams, over one big season of 38 games, because league tables never lie.
Whereas KO competitions sometimes lie If Spurs won it at the final, were they the best team in Europe? Even as a fan I will laugh to say this
However, if we are talking about simply just Spurs or even any other team in premier league that has been away from winning anything, I would assume that you would be right, any team that did not win anything for the past decade or two and even longer or maybe never may want premier league a bit more. Even in that situation it is not 100% clear, I would assume they would be thorn apart to decide on that.