I suspect that Heathrow's new-found enthusiasm for expanding regional connectivity would evaporate pretty quickly if the regulators insisted that slots that could otherwise be used for longhaul widebodies were instead reserved for regionals with their Dash 8s and ERJs.
With a third rwy, using slots for "this"
OR "that" will no longer be an issue, sufficient slots will be available for "this"
AND "that", this is the point. Both will be needed, longhaul routes need shorthaul feed.
Also, there will be no foreign interference from Brussels, the government will be free to decide whether (or not) some slots for thin domestic routes would be ringfenced, which routes would have have PSO status, levels of caps on airport charges, etc.etc..