> no HSM would ever generate these
You trust the magic black box far more than I do.
My big fear about HSM is that they are inscrutable by design. There is no way to verify they are working as advertised. Plus side, all sorts of fancy hardware to protect your keys. Down side, all sorts of fancy hardware that obscures flaws in the implementation.
I think I'd prefer open source hardware built from off the shelf components glued into a secure enclosure. That way you can destructively audit a few at random if the application matters enough to justify the cost.