I am always in Cup a couple levels above, but I was surprised the first time.
I think you might want to read this to avoid other surprises (as well as some of the Tutorials and Guides on here) Top Eleven Official Wiki

Players lose some value at the beginning of a Season, as they are older, but I still buy late in the Season because I hate bidding wars. As you play and train them and apply skill points their value goes up. The players with the highest values do train faster than others and are worth having (even on a team than doesn't buy tokens) because you can have them a few seasons or more. I train my guys a lot so I can keep them longer.

You can succeed in Cup as you described, but for me that would ruin my team. I carry a full squad to compete in Champs League, League and Cup, and it's just me but I like all 22 guys I have and can't imagine replacing them seasonally. Also for me putting a bunch of new guys out, you have no idea how well they are going to play. I like adding one or two new guys at a time to see how they do.