A guess at the reason
This is just a guess at the reason - I don't know if it has any validity/merit...
The City CTR contains a huge number of buildings/areas of national importance...
The City of London
Houses of Parliament
Canary Wharf
Buckingham Palace is a stone's throw away
And many, many, many more.
Also a large proportion of the zone is very built up, not just R160.
If the airspace was completely unregulated (/unmonitored) in a free-for-all then I suspect various security agencies would be somewhat twitchy.
Not that I'm saying that a simple prior phone call would prevent a "nutter" from causing mayhem, but it may mean that the total number of flights, and the associated risks of collision, particularly in the vicinity of these important areas is, in some way, mitigated by regulating traffic.
If that means a sight-seeing tour, or other non-standard flights, are delayed to a more appropriate time then that seems a reasonable response. We are not talking about open countryside here where the risk to people on the ground is minimal.
There may be some merit in de-classifying a portion of the zone (let's say, for example, the area to the east of a north-south line through City Airport) outside the airport operating hours however, this also creates the potential for problems at changeover times from regulated to non-regulated airspace (or vice versa). Sometimes published operating hours are extended (albeit these are covered by NOTAM...but often only issued very close to the published closing time) leading to a possibility of confusion as to whether the zone is regulated/non-regulated.
Where to draw any particular line in the zone would inevitably open a can of worms. This combined with confusion regarding opening/closing times, in my opinion is a recipe for confusion. So, again in my mind, the current arrangements seem preferable.
Although ATC is not a policing force it is there to provide a safe service to aircraft (how far does duty of care extend?). When it is not possible to maintain that level of safety then some form of regulation is surely necessary. At the moment, as I understand it, non-standard flight applications are to be submitted in advance of the planned sortie. Somebody, somewhere assesses each flight against all other known flights in the area at the time and makes a judgement call on whether the number, and complexity, of flights is acceptable in terms of ATC's ability to provide their service. Does ATC have a responsibility to separate VFR flights within Class D? Clearly no. That is the pilots responsibility, but ATC do have a duty to pass pertinent traffic information. When traffic is so dense that pertinent traffic cannot be passed then ATC would have failed to provide the necessary service.
The status quo, in my opinion, is the most sensible option. With airspace users on non-standard flights notifying the powers that be of their intentions before taking to the skies. If the powers that be suggest altering flight times to avoid congestion then that is most likely to mean that the operator can get on with his/her flight in relative peace and quiet...something both parties would eminently prefer.
Again these are just my thoughts, I am open to better understanding and more appreciation of other peoples thoughts.