Main aspect of circuit designing process
This is a very thoughtful statement and reflects my own experience going through a EE degree.

Circuit analysis ("solving circuit problems") is the foundation on which circuit design/synthesis is built upon.  You can't really build something if you can't analyze it. (eg. you can't build a car if you can't diagnose simple car problems or list the different parts inside a car).

A lot of undergraduate work is learning the fundamental building blocks and theory of modern circuits.  Amplifiers, digital logic, filter design, board design, antenna design, wave propagation, etc.  You might not necessarily use all of it in your career, but you at least know the core components of modern circuits and are better equipped to modify an existing design when you encounter it, or design something better.

It's unfortunate that all this information comes piecemeal at university.  You don't see the big picture until you're a junior or senior.  At least, that's how it was for me.  Good luck in your studies-- don't feel bad if you don't see how it all comes together right now.  I've been there myself.