Trying to get an apartment inside Windsor Castle was one of the more strategic moves they tried and I’m not surprised it was quickly shut down.
Inviting people (A list celebrities) to visit you in a castle like Windsor - even if you only have a small apartment there - looks a lot more impressive than tiny Nott Cottage in KP or even the bigger apartment in KP.
They would also have been in ‘popping round’ distance of the Queen when she was at Windsor - which they could have used to their advantage - for actual influence or even just implied influence.
Lastly - Windsor has always been the home of the monarch - but imagine if they’d stayed and been firmly installed in Windsor by the time William came to the throne - it would have almost become ‘their patch’ - ‘their court’ - they would look like they were letting William stay occasionally in their home.
It was a power move that the Queen’s advisors saw through immediately.