DFC
I have never heard a request to leave controlled airspace denied and very seldom delayed. However, trying to get back in again 100nm down the road can take longer and burn more fuel that was saved by the direct leg.
I have heard controllers deny directs outside of CAS due to extensive military activity. When I last flew in that part of the world it did happen now and again. Perfectly understandable.
Piltdown Man
I used to work for an operator who filed and still do file a significant portion of their flights (East Coast UK) outside CAS and this was not helped with the alternatives sometimes simply not being possible from a fuel/range point of view.
Whilst flying for that operator, I had an RA with a F3 from Leuchars. It passed a couple of hundred feet above us with his colleague being slightly more generous and passed a few hundred feet below. I think it would be fair to say that the F3 drivers knew about us since why would they have gone to the effort of providing a lovely fly past? The modus operandi of our military friends is to 'see and literally avoid'. I am sure that most military drivers will happily and perhaps unknowingly erode the comfort zone of most civilian pilots, when it comes to separation in the open FIR.
Maybe that is why the pax were served complimentary champers and sloe gin -
"Was that a formation of Tornados that I just saw pass us?" 
It is simply not worth it and as for nipping off to OTR on a short cut - you would be surprised at how many airlines no longer file any of their flights outside CAS direct to OTR. This applies especially to Newcastle and Teeside departures.
Anyway... if you want to see creative ways in which capacity is handled. Come to Africa where there is a fraction of the movements and they manage to make a real horlicks of it!
