I think you are absolutely on the right track, but in my view the problem is less tightly coupled to the funding and more institutional. As a professor it is s

I think you are absolutely on the right track, but in my view the problem is less tightly coupled to the funding and more institutional. As a professor it is simply extremely unnatural to just drop your main area of research. First, your academic network will almost entirely stem from the subfield you have been working on. This affects the expectations of your PhD students, the recruitment of postdocs (who are often swapped between colleagues in the subfield), and the conferences you visit -- where you will see all the familiar faces of colleagues you have known for years. Second, your mind has been shaped significantly by years of working in your own little subfield. It is easy to come up with ten projects in your area, rank them by difficulty as well as the interest they would generate amongst your colleagues, and help your students to execute them. It is significantly harder to do anything like that outside your subfield; for one, you will not have the mentoring that a typical PhD student has.