Pierre, if your vehicle is no longer on the system, or if the last rego number is unknown, you need to have an ID inspection (but not a roadworthy), that's just the way it is, cars too.
A club inspector is basically only authorised to recommend a "known" (on the system) vehicle for club rego, through one specific club that both the inspector and vehicle owner are both financial members of. A vehicle cannot be registered unless it is on the system, and it needs to be put on the system by someone authorised to do so.
While the ID inspection does cover the same details, because the vehicle is an "unknown" vehicle (no plates/not easily identifiable), they also run the numbers to check that the vehicle isn't stolen, not usually an issue with historic vehicles that have been out of rego for decades but more so when someone turns up for an inspection with a VZ Commodore with no plates and no history.
The ID inspection is performed by someone who is authorised to recommend a vehicle onto the state rego system in the first place, from where you can then apply (through a club) for club rego.
I have had to have ID inspections done for a couple of old trucks. I had the ID inspection done first, then the club inspection, then took both forms into Service SA, the ID form puts the vehicle on the system, the club MR334 then registers it through your particular club, no hassles.
