What is the advantage in viewing final semantics as a metamodel. That is we can view computational objects operationally as transition systems. What we do is we try to capture the operational behaviour of a system through a suitable functor F. And then we focus on a given observational equivalence. This essentially amounts to finding that final model which expresses the intended operational behaviour.
And we get a characterisation of a sort of a minimal automaton-like characterisation of our semantics.