The chassis of the Morgan is basically a ladder chassis, but instead of I beam, Box section or tube it's made of Z section steel. I assume it's done like this to make it easy to manufacture. Especially as this technique has been used from the initial designs.
It has little triagulation amongst it's key components, basic ladder, bulkhead and cross head.
The Ash reinforcement which is bolted down each side of the chassis under the main tub is put in to strengthen the chassis but allow flex.
Think of the chassis as 1/3's
Rear third, mounts and supports the rear axle
Centre third main tub and passenger compartment
Front third engine compartment and mount for the front suspension via the cross frame
To a certain extent the flex is esentially "built in"
Advantage:
Gives a slighly more supple ride, making up for drawbacks of rudimentary suspension.
There was a space frame supplimentary chassis used in one one racer I recall. ie. original chassis, with a second bolted to it to instill regidity.
I think the Big Blue +8 racer had a space frame chassis with honeycombe structural pannels.
Moving to a more modern and rigid chassis type would basically superceed the suspension both front and rear and introduce weight.
So wilst not perfect it gets the job done, all be it, in a traditional type way... which after all is what Morgan is all about.
For a comparison to effectiveness, just think about a similar output Lotus Elise. Similar weight, power output (ok slightly better aerodynamics). The lap-times and driving comfort are significantly better..... look at the differences in design as to why.