To speak to the question raised in the comments of if top universities have interdisciplinary professors, I graduated from the University of Chicago which has many professors with multiple/cross-disciplinary appointments.
In fact, we have entire programs that are interdisciplinary, such as the undergraduate Computational and Applied Mathematics (mathematics, computer science, and statistics) and the graduate Committee on Social Thought (philosophy, politics, and sociology). There are professors who are specifically appointed to these programs / departments.
We also have professors with postings in multiple departments. We have at least four professors who have appointments in both mathematics and computer science. A number of our computational linguists have linguistics/CS appointments. Our philosophy faculty have overlap with our Divinity school. I believe we have a professor who does quantum mechanics research who is appointed to both chemistry and physics. These professors hold such titles seperate my. For example: Alan Turing, PhD. Professor of Mathematics. Professor of Computer Science.
Yes there can be reservations about the depth of knowledge of people with interdisciplinary degrees, but if you're interested in doing interdisciplinary work then an interdisciplinary degree is a great thing to have.