I’m fairly sure that Morgans have always had a steel chassis; the ash frame essentially supports the coachwork rather than primary dynamic loads. The Morgan as a 'wooden car' is something of a myth.
The first picture in the original post: that is truly a woodworker’s car in it’s entirety. Somewhere (and I will try to find it*) I have kept an extensive article on that machine from the now-defunct Cars & Car Conversions magazine (“Triple C”). It was - fittingly - made by a guy named Friend Wood (real name, not a deed-poll change - maybe that’s a case of nominative-determinism?).
Wooden monocoque chassis have not been particularly uncommon in a motor sport context, historically at least; these have typically been moulded-plywood structures.
Marcos, Nathan and others have done this. There was a fairly well-functioning Formula 2 car in the sixties - the Costin Protos: this drew on the aircraft industry experience of its creator, the ex-de Havilland aerodynamicist Frank Costin - who also worked on ground-breaking Vanwall and Lotus Grand Prix cars. (Frank’s brother Mike, another early Lotus collaborator, is the ‘Cos’ of Cosworth.)
The first McLaren designed for Grand Prix racing, from 1966, featured a chassis made from ‘Mallite’ which is a composite comprising two thin skins of duralumin either side of layer of end-grain balsa wood.
Not exactly wood, but the pre-war German marque Hanomag had a version of their small vehicle (nicknamed ‘Kommissbot’) which had wicker coachwork. The name came from its perceived appearance as a loaf of army-issue bread.
(*This week’s project, I guess…)
