here's my take - fwiw!!
The estimate could assist in planning from our perspective, mainly in managing the 6 aircraft we can have. If a lot call, it's quite simple to not launch any until we can have the six. That would be my guess.
I think the estimate is a direct reaction to the 2RN mid-air. Aircraft can hear each other approaching the reporting point from different directions rather than running into each other just as they make a call (I think that's the theory). Nothing to do with ATC managing the cap - plenty of time for that from the inbound call - see below:
My understanding (which may change once I am back there) is that the six aircraft includes inbound and outbound aircraft. I think that essentially limits us to the number of aircraft in the CTR
it certainly says "in the circuit" - open to a little bit of interpretation. Number 7 departing leaves "the circuit" (late crosswind etc) - number 8 can go.
You could have more than 6 inbound as long as the first couple land before the last ones reach "the circuit".
I think you could in theory have 8 or 9 on frequency on each side.