Why is a system description in control theory important?
No, it sometimes isn't enough to just have a feedback loop.  An understanding of the underlying system will let you know before you put in a lot of effort what the best you can do is, or whether a system is controllable at all, to let you know if its worth trying.  After that, you could compare a system to it's ideal behavior to let you know if you're getting the results you should.

That said, there are a variety of systems that are not tricky, and where you don't expect many irregularities.  Such systems can usually be satisfactorily controlled with off-the-shelf devices with confidence.