Compared with the phone itself?! Hardly.

If a case gives you even six months' more use of your phone, because you don't break it, then it's an environment win.

To be honest, I never use a case, but that's because I rely on never dropping my phone (so far, so good!), and that's because I always wear jackets and put my phone in a side pocket where it can't fall out.

I recommend using a case to everyone. Phones are expensive and, as you point out, not designed to last. Most people's experience is that a $15 case will increase the lifespan of their $200 to $1000 phone substantially.