Are interdisciplinary STEM PhDs qualified to become professors?
Yes, interdisciplinary Ph.D.'s are qualified to end up in academia.  In fact, I think hiring interdisciplinary faculty is a quite a popular idea with university administrations, and so my feeling is that there has been a bit of a burst of interdisciplinary positions created.  If you do really excellent interdisciplinary research, I think you should have a very good chance of getting an academic job.   

I think you do correctly note some disadvantages that come along with it: hiring and tenure decisions tend to be made within departments, and interdisciplinary work can sometimes look not especially deep from the perspective of either of the disciplines, or simply be difficult to see the importance of if you don't see both perspectives.  But if people really do come to see the connection, then it will be highly valued.