Yeah I came to the same conclusion.
Universities use all kinds of hard to setup stuff which are often custom built. Slurm configs, custom configured HPC servers etc. All of this pays off though if you need to do heavy computations which a local machine won't do.
IMO it would be better to make Claude build out something that makes interacting with the HPC much easier. A web UI, Tailscale whatever.
I mean Open OnDemand has been built for that purpose and is deployed in like 2000 locations at this point.
https://www.openondemand.org/