I'm a strong advocate for migrating research code to FOSS wherever possible, but even I don't agree with this statement. Mathematica and Matlab are pretty good at what they do (labview is a different story).
What "vastly superior" FOSS solutions do you have in mind? sympy? sage? Do you think these aren't going to have errors in them?
Depends on the problem domain. A good example is 1D numerical perturbation theory; my colleagues struggle to beat mathematica over the head until it gives them roughly what they want. On the other hand, it's much easier using jupyter, numpy, and matplotlib.
>Do you think these aren't going to have errors in them?
Of course they do, but they won't go unfixed for years on end. You can also figure out what's wrong without having to reverse engineer a big binary blob.
In my experience, it seems to happen because those are the tools taught to science and engineering students, who then take them to the workforce (post-doc, industry, etc.). Those entering academia then use them for instruction, rinse & repeat, just like you describe.
For what its worth, I've tried very hard to move folks I work with from MATLAB to Python.
Here's a good reddit thread about some really terrible arithmetic errors in mathematica: https://m.reddit.com/r/math/comments/2kjyrc/known_error_in_m...
As a computer scientist doing physics research, I don't understand how my colleagues put up with the terrible trifecta of mathematica, matlab, and labview. These are some of the lowest-quality and most frustrating pieces of software I have ever had to put up with, yet they are ubiquitous in many research communities. There are vastly superior solutions that are free, open-source, and, as far as I can tell, much easier to use.
Every day I see students and researchers struggling to circumvent the idiosyncratic and senseless designs of these softwares. I think it might just be a vicious cycle of professors only knowing shitty software, so the students only use shitty software, don't learn good software, become professors, and the cycle repeats.