I learned that this ticket exists via this thread - sounds interesting.
I think growing up in EMU land, I viewed HSTs as something that there was a premium for. This would be from the rarity of being able to use one, and the route using them (for me) being Via London adding that premium.
NRE shows the tickets being valid on GWR, and that the info was last updated in February. I'm guessing that TfL Rail West is not valid on this ticket (as far as H&H), rather than just the NRE page not being updated?