A PhD can give you an opportunity to work on what you call a "real" problem, but it could also force you to work on "fake" problems. In many fields, the research we academics must do to get hired/promoted/tenured is somewhat artificial and unrelated to the problems we're in the classroom teaching our students to solve. On the other hand there are great stories of PhD candidates starting businesses. I think Google got its start as somebody's dissertation.

When considering a PhD, the best thing to do is look at the advisor(s) you'd be working for and their repertoire of projects. Looking at the "discipline" isn't precise enough; there's a wide range of stuff happening within fields like information systems or computer science, everything from very theoretical to very practical.