As it turns out it doesn’t actually cost that much on regular transit, there’s an AIRPORT SURCHARGE because it’s an “airport train”.
No wonder Americans don’t use public transit, even when the system exists it’s ridiculously difficult and expensive to use.
I didn’t use them, so no idea if they are nicer - but they were quite a bit faster, yes.
Pro tip for London: You can swipe your credit card at the entry and exit points of your underground travels and it will cost you much less then any tourist tickets they sell.