Well, the thing is even if you trace it back to an account, what do you do then? Only a single pirate with a bit of opsec knowledge needs to have an account with e.g. a stolen credit card or whatever, and then they can just leak everything with no consequences…

Yes, but we aren’t talking about the limit of the volume. We are talking about volume in actually infinite dimensional space.

This reasoning is pretty weird, but the conclusion is basically right. That is, there is absolutely no way to extend the conventional notion of volume to Rinfinity, which is basically what most people would imagine is the infinite equivalent of our dimensional space. Edit: what I mean by Rinfinity is a bit ambiguous, but let’s say for the purpose of a hypersphere we want something like l^2 hilbert space to ensure no vectors with infinite length appear, then we have a separable space and the proof is complete.