Please could you explain how much journey time will be saved along these sections, as a result of being served by HS2? After all, you've presented it as serving "a lot more than 100 miles" ...
Sorry, but how are those claims of yours worth the cost of £100bn?
The question was does it provide journey time savings beyond the 100 miles, you've now asked a different question given that you clearly don't like the answer.
As to the cost, clearly the two examples aren't worth £100bn.
However, there's a lot more than those examples.
However, I suspect that whatever anyone says chances are you'll disagree with what is said.
Anyway, the main point I keep coming back to, is that passenger growth is still broadly on track even with a significant change in travel patterns and the delay of in opening HS2 means that the growth can be zero and still carry the same (or more) passengers than was expected to be the case upon the original start date.
The proposals for an HS2 'Heathrow Hub' appear to still have it on the GWML rather than any closer to the airport. I'm not sure that gains a great deal over Old Oak Common, which has the potential for onward connectivity to more of London.
Old Oak Common will likely be sufficiently useful as per this post:
Heathrow Hub as the first HS2 stop out of London would only have been a superior option to Old Oak if:
a) the GWML was diverted via Heathrow ie a Paddington to Bristol/Cardiff/Exeter train would call at Heathrow as its first stop out of London
b) all or most Crossrail services went through this Heathrow station, possibly rejoining what would have been the “old” GWML to continue to Reading
c) HS2 took a very different route, requiring a rather awkward curve.
Seeing as both A and C and probably B seem ruinously expensive and disruptive, it is hard to see how this would have worked.
The real issue is that London’s main airport is in the wrong place- it should be either at Luton or in the Chilterns- but then we are getting way into hypotheticals.
Although there's more that it could also do.
First up there's a lot of development due to happen nearby.
There's also possibly further rail schemes (such as Overground services nearby at Old Oak Common Lane and possibly HEX services passing through Heathrow if that happens).
Heathrow Hub could have worked I think. It was near enough to Heathrow to plausibly feel like part of the Heathrow complex. Whereas OOC is a whole borough away. If it was built at Stockley Park, you could have had potentially 6 Crossrail trains an hour connecting from the airport to the terminals. New York's JFK has no rail connections at all, but relies on (admittedly unacceptably long) driverless light rail lines to connect to the nearest rail nodes. We didn't have to route HS2 underneath or beside Heathrow itself.
Heathrow Hub would have also provided parking near the M25 and rail connections to Surrey, in theory, with the Heathrow Southern Rail Link. Not all trains would need to stop there. I doubt there would be much demand for Leeds/Birmingham trains, but certainly the Anglo-Scot or Manchester trains.
Southern Approach to Heathrow (depending on which services are the through services - either the Metro or outer suburban routes).
The Metro services could cause issues with the potential of inheriting delays between two very complex areas (whist this is also true for the Outer Suburban Services to Guildford and Basingstoke the lines are less intensely used and so have more scope for recovery). There would be limited benefits in terms of station pairing due to the interchange options at Clapham Junction and Richmond (and a lesser extent Kew).
Pairing Woking, Guildford and Basingstoke to Paddington would give quite a significant population direct rail services to Old Oak Common and HS2.
This could put Woking, Basingstoke and Guildford within about 150 minutes (even with only phase 1) of Manchester. That makes it around 60 minutes faster than current services.
That makes day trips viable (leave Basingstoke 8:30, arrive Manchester 11:00, leave Manchester 18:30 arrive back 21:00) without having to leave early and arrive back overly late.