Yes, its done already in some new boats. 0 wood in the structure.
It tends to come out heavier.
As far back at least as the 1960's (maybe earlier) some fiberglass boats used metal stringers.
The newer boats without wood often have shaped/hollow fiberglass structure forming essentially square boxes. The glass is considerably thicker than if there was a wood stringer inside.
Yes, if I were to do a full cut and gut on a boat, I would use synthetic instead of wood. A key challenge is that the synthetic core materials tend to be pricey and that is one of the reasons you still see lots of wood used.
A product called 'Divinycell' is used by some boat manufacturers for stringers and bulkheads. Another product called 'nida core' would be better for decking and transoms that have compression loads.
There is also a product called 'coosa board' which has applications in boat structures as well.
You can also use seacast if you create a cavity that it can be poured into. It works great but is pricey but Never rots. Wood of course is the simplest and cheapest. I have two seacast boats and wouldn't do it any other way. Just a preference on my part.