Mathematica notebooks are used work with symbolic problems more often than not. HPC is more numerical. If someone uses Mathematica to check equations, looks up solutions to ODEs, or calculates a Jacobian which gets implemented in code you will never hear people say they used Mathematica for it.
By far the largest number of users (not core hours) on both of HPC systems I manage are using Python or R. A lot of them use Jupyter and RStudio through an OpenStack instance. So they're using exactly the sort of notebook interface you're talking about, coupled to 40/72 core nodes with 256/512gb of RAM.
I'm well aware of what Mathematica is capable of, I made use of it for all sorts of things in my research career. I used it a lot for generating input configurations for molecular dynamics simulations, plotting, symbolic algebra, generating Voronoi diagrams in post-processing of simulation data and more. All of that ran on a HPC cluster as part of the pipelines.