You are absolutely correct. The League Cup is a great trophy to win if it adds something to an already great campaign like a title and a Cup for example or if it is a part of an extended run of winning trophies year in year out. But on its own, it's not gonna indicate a team is progressing or doing well if the league campaign is a failure. If Spurs finish the season without competing for the title or worse, outside the top 4 and win the LC, nobody is going to praise it as improvement, just look at Arsenal, 3 FA Cups in 4 years and nobody seems to care.