Hi Phil
in principe you are right, however vessels can have no classification.
Unlikly though. Reason: A owner can build a ship as long he follows the rules. The real problem would start for him that P and I and Hull/damage insurance will not insure the ship
that easy. so the easiest way to do it to let it classify by a IACS member, like you said,, ABS-NKK, DNV-GL, LR and so on.
the other thing charterers will not so easy charter /employ a ship without classification
and cargo operators only,,like voyage charters, what we do a lot,, Like ADM/Cargill etc they will also not take ships with no class.
Ships registered in "not so perfect countries" and will say trading only within the countries limits have often no class anymore.
Class withdrawn means either as you stated change of class, or really withdrawn because
sub standard and/or sold and nobody knows. Laid-up can be too,, yearly surveys cost a lot money,,so if longer times laid-up,, they could let lapse the surveys, and then re-survey once the ships moving again.