Steering not aligned with front wheels

I got the front wheels of my car aligned because I hhe need steering toward left to go straight. It became better but was slightly off, so I went back to the same shop to complain. They said it might be because of the right and left tires worn unevenly. And then they found that some parts that connect between steering wheel and wheels got bad and replacing it would cost me $300, Leaving it as is would result shorten the life of the tires.
Question - Should I do it? What could go bad between wheels?