<<The idea to put them all in the same room was to make co-ordination between them and the preceding TMA sectors more efficient.>>
But the original idea of integrating the positions didn't work, as proved by simulation, so the Approach controllers still sit quite separately from the TMA people.
I moved with Heathrow Approach to TC and spent 10 years there before retiring. Apart from a fairly nice coffee bar and a bigger car park I never found any logical reason for going to LATCC. On the contrary, the extreme lack of radar awareness of the new Tower controllers at Heathrow often concerned me. Probably the Heathrow people found that the newer radar controllers showed an ignorance of their problems too.
Sure, we sat in the same room as the TMA people, but not close enough to converse directly so all liaison was carried out by telephone, as when we were at the tower building. We might see the odd (some very odd!) TMA controller in the rest-room or canteen but conversation did not always centre on "work" so there was little benefit in that direction.
Nobody has ever provided me with a truly sensible ATC reason/argument for splitting the Approach and Tower functions but I'm still listening (just out of curiosity now). Some (me included) found tower work harder as we got older and radar was far more leisurely... but others had opposing views.