Completely agree. I had the chance to be on project where I was the least experienced in programming, and got to deal with the management stuff (in the most basic meaning: I was doing just anything needed to let the other devs focus on their tasks, not telling other people how to do their jobs). I learned a lot, I got explained a lot of tricky problems that I wouldn't have understood otherwise, and on their side they didn't have to care if the client answered their email or not.

It was a really nice experience, but more an exception than the rule. I never got to work in another place where people wouldn't focus on the titles as a hierarchy thing, but just as different roles in a projet.