Where are the pathways on HS2 for the trains to go North-Airports-Europe? It's a key part of their business case for the line, but either frequency to London from a core city would have to be reduced, or fewer Northern destinations served by HS2 if they want to have avoid-London running. Neither can be easily justified here.
Also, I highly doubt a high-speed line running North-Heathrow-Gatwick-Ashford-Europe will take much traffic off the M25, where traffic is more regional. Ditto any HS1-HS2 link (cf the Greengauge report that had only about a sixth of traffic not starting/ending in the SE, and over half not actually leaving it).
Heathwick is not a solution to the airport capacity gap. While their complaints about being 'full' are laughable given the year-on-year continued growth in traffic at both airports, no extra capacity has been created and utilisation is soon going to hit a hard barrier: there's only so much more than can be squeezed out of those three runways. Either have both airports as competing 2-runway hub airports that are top-10 globally for traffic, or have Heathrow as a 3-runway uber-hub 130% the traffic of its nearest competitor (Atlanta, or Dubai) and Gatwick reduced to Stansted/Manchester levels of traffic.
It's all stuff that looks good at first glance, but doesn't bare scrutiny well.
PS: a super hub airport is similarly sensible-looking, but silly. It's like a single Hauptbahnhof for London - there's too much traffic to send through one place, just with consolidation and without the extra transfer traffic. And that's before you get to single-point-of-failure issues where a small fire (or whatever) can cripple a whole mode because the eggs have been put in one basket and that basket has been dropped.