Welcome Doug,
Just another few points to ponder for you
Quite often the CTOT you are issued is not directly related to LHR and may actually be a restriction due to en route capacity issues. Whilst the company Ops people can access what airspace is causing the maximum delay to your flight, it may not always be obvious to the flight deck.
With that in mind, clever people have also worked out that the way to maximise the arrival rate at LHR is to have a reservoir of aircraft in the holds there. This allows the controllers to pick and choose aircraft for the arrival stream without wasting any gaps which might occur if they stuck to and enforced the 'published' arrival rate, given the inaccuracy of this as a blunt tool since the size of the CTOT window and the time which aircraft can gain or lose en route, particularly over long distances, is something which does not lend itself to guaranteeing a smooth and consistently spaced arrival stream.
Your final point is always an interesting one. Technologically, it should be possible for a real time automated system to monitor aircraft all over the globe inbound to LHR (as well as to everywhere else), issue 4D flight path clearances, monitor for compliance, and then issue amended clearances for traffic to operate over waypoints or gates +/- a few seconds. Probably not a big deal to Airbus guys whose throttles don't move, but Boeing guys might get dizzy seeing them move backwards and forwards continually as the speed changes are demanded
.
One of the main hurdles to this is money since you will have to pay for the development of the kit, provide it to every 'ATC' facility in the world since everyone will have to integrate their local problems with every other aircraft on the globe, and then get operators to equip so they are capable of flying in such a system. Then you have the problem of airlines planning their flights to all arrive and depart at similar times. Regardless of technology, you can still only get one aircraft on the runway at a time (yeah I know ... land after and conditional line ups exist, but you get the point) , or at a given position in a queue taxying for departure or a stand. In other words, although we can tweak the system today and go for some sort of 'free flight' concept in en route airspace 'tomorrow', the terminal areas will remain somewhere where the differences between what is theoretically possible and what is realistically achievable practically, will remain a long way apart for the foreseeable future.