A delay to completing things like surfacing roads and footpaths, streetlights and other planning requirements such as play areas are frequently left unfinished or not even started for years.
The simple reason being that these do not give any profit to housebuilders. In fact they are a cost.
Add in that once the last home is built and has moved in the site manager, the driving force for getting work done on the site, is moved to his new site.
Any outstanding works are viewed as low priority and the incompetence of those who work at regional offices and customer care only serve to add to the problem.
I know of one development where the roads and streetlights were not finished for 10 years!
Also
Taylor Wimpey were featured on BBC Watchdog in 2012 one of the issues being uncompleted play areas!
It just proves this issue isn't being addressed by housebuilders.
You do have recourse to complain to the council, which given it is now over five years ago I expect you have done.
So the question is, why haven't the council enforced the planning conditions and either got Persimmon to build the play area or employed another contractor to do this and charged the cost to Persimmon?
There are council elections on May 4th, I suggest you don't vote for any sitting candidates.