If someone graduates from a game design program, I don’t even know if they’d be qualified for a code monkey position. If your job is actually doing game design, then you do have some creative input - you will be shaping the game. If you join a larger company, it’ll take significant time and luck before you’re a design lead, but even in a junior position, you can make a difference both in your own work and in conversations with your co-workers
ETA: I agree, though, that if you just want to make a game to express your vision (and not necessarily have game making as your primary income in the near future), there are a lot cheap or free ways to pursue that
