I disagree that it's undesirable for back-up and restore to be impossible in all cases.

Instead, I would argue that plain-text export of private and secret keys is undesirable, as it removes any protections the HSM was supposed to provide (2 man rule for access, audit of use, etc). Back-up schemes that export these keys (in encrypted form) to another HSM that enforces the same rules as the original HSM can be useful, IMO.