There is no guarantee that expansion at Heathrow will improve its connectivity to UK regions, The Airports Commission forecasts the opposite - that the number of UK destinations served from LHR will shrink from the current 7 to 4 within the next 15 years, even with R3
Considering the runway, would not even be operational within that time they may well be right. I hardly think the likes of Flybe and Easyjet would not want to fly into an expanded LHR though carrying all that connecting traffic from the UK and Europe.
Also why do people keep putting down LHR based on it's current transfer connections. The whole point of this plan is to build and improve the airport. Something is already well underway and it has the potential to become a world leading facility.
But of course we can't have that can we.