I guess I assumed you were inferring that orthoses immobilised feet given you mentioned both these things in the same sentence and likened them to a plaster cast which of course does immobilise... ?
Thinking of orthoses as "providing external support" is a little outdated and not quite as scientific as it should be. They actually have far more profound kinetic effects. They can manipulate the magnitudes, vectors and temporal patterns of plantar reaction forces and when used in the right hands with the right understanding of their mechanical effects they can be the difference between the ability to be able to run pain and injury free and not.
I'm not sure how you define an "average runner" but I assure you that whilst orthoses are certainly not appropriate for everyone, there are many runners who will need them on a permanent basis and could not run without them.
Ok, plaster cast was a bad example to give - that will fully immobilise a joint, and of course orthotics won't do that. It would have been better to have likened them to a pair of crutches - they can have a profound effect on kinetics and manipulate the magnitudes, vectors and temporal patterns of plantar reaction forces of someone who is partial weight bearing as well.
I'd agree orthoses design & production and gait analysis has come a long way since the simple 2-D "upside-down pendulum model" I was taught as an undergraduate and rightly so. It does make orthoses more fit for purpose - but doesn't change their purpose.
I'd still be inclined to try and wean the average runner off them after symptoms have eased if I can. I'd define the average runner as anyone who does not have arthritic or ossified joints, major abnormal foot anatomy or any form of muscle wastage disease, MS etc... I'd refer them in this case.