More like building shared infra to get at a better and more efficent end of scaling laws, than having many small clusters all over. I don't think it really is a privacy question but just a way more economical solution.
Basically make your own hpc provider for academic purposes, and rent out extra capacity to smaller commercial interests to utilise that spare capacity and also prop up the local economy with usable research compute.
Here it is not the privacy concern of the user but that of third parties (e.g. those in medical images). And yes I am a strong advocate of using shared infrastructure for this rather than letting some PhD student handle this a part of their research (which is the reality with lab clusters)
You're building a common infrastructure to address privacy concerns about the use of shared infrastructure??
Basically make your own hpc provider for academic purposes, and rent out extra capacity to smaller commercial interests to utilise that spare capacity and also prop up the local economy with usable research compute.