If it's OK to have an enormously long runway and use one half for landing and the other half for take-off (the "runway extension" proposal that's on the Airports Commission's shortlist), what would the prospects be for dividing one existing runway into 2 * 6000' runways and using them for aircraft of a suitable size?
It hasn't yet been established if it's "OK". Even the proponents of the scheme admit that the safety case is far from proven.
And aside from that, the proportion of Heathrow movements that could operate satisfactorily from an 1800m runway is pretty small.
What happens when an aircraft is taking off on the western end at the same time as an aircraft landing on the eastern end gets into trouble and needs to do a "go around"?
If landings and takeoffs are not simultaneous on this system, there's no point, as the overall increase in movements will be insufficient to justify the investment costs.