A fast link that allowed terminal to terminal connections between LGW and LHR could actually work quite well for transit passengers
No it wouldn't. It would be a complete disaster and just about the worst possible outcome. Not to mention the nimbies on this fast rail route would never let it happen.
A 30 minute frequent airside link wouldn't be so much worse than the inter-terminal transfers at LHR over the years where a 150 or 180 minute connection time could easily be consumed by the queues and congestion.
Over which years exactly? When was the last time you transited through LHR? You are basing a proposed new project on the past case. LHR is in the middle of a complete rebuild and it is becoming a world class airport.