Heathrow inbounds normally drop to 4,000' initially droping to 3,000 close to the centre line and climb unrestricted to 6,000, normally at a very good rate. Only go-arounds climb to 3,000' (or 2,000')
SFC > 4000 Approach and go around traffic
SFC > 6000 SIDS
4000 > 8000 Intermediate approach/departures
8000+ Stacks
I can't see where the space is that you propose
Departures only have to make 4000' by Beaconsfield when they leave the CTR to the north or 4000' over Epsom to the south. A 400 tonne jumbo just about makes this restriction and there are plenty of those that depart everyday.
Separation laterally and vertically is required, not only to avoid intimate aluminium but for wake. I wouldn't fancy being 500' under any commercial jet in my 172 as the "heavy" passes in climb/descent nor level flight less than 200 yards from me.