I would guess that a C++ codebase written by PhD students, not by seasoned C++ experts, is more complicated and much slower to debug, than a corresponding Fortran codebase.
No, I'm not kidding.
I shudder to think what they'd have done with C++. :-)
Function has its side effects. It's use as only once case is really questionable, justified by lack of other means.
So especially in the hands of non-experts, Fortran should produce less bugs.
I don't know of any studies like this. But there are two aspects to consider. One is what you've pointed out, which is the long-term scientific gains and the productivity of the research group as an entity. But the other aspect is whether those students who rewrote the code into C++ were more or less successful than the students who weren't rewriting code.
Obviously, how you judge success in the latter will be tricky, since there may be differences in the interest of students who rewrote the code and their desired outcome after the PhD (e.g., stay in academia versus go into industry).