Mango
That was really interesting to read, and I am surprised that there is not more financial benefit to having a Royal patron - although it is one report.
I thought it was good to see that 36% of the charity time given, was to organisations that had been set up by the Royal in question - makes sense that they support issues they are specifically interested in.
I suppose the option is always there for the Royal Patrons to be dropped, if they offer no benefit, although (with the exception of Andrew?), I can't recall that happening. The QM was Patron of a school near me, and Edward has now taken over. He has visited a couple of times, and it certainly gives the school a boost, with the children all coming out to wave at the helicopter - and the associated press coverage. Minor thing, but a boost to many in the community, and nice pictures for the local paper.
There is also the benefit to charity staff morale, and the fact that RF involvement offers a level of comfort to potential donors, as they assume the RF will have checked out the charities for any 'uncomfortable' issues. Obviously this has not always been reliable! 
Ed Sheeran is incredibly generous - hats off to him. Many celebs not so much. As it's private, we'll never know what donations HM makes.
I do think that one important thing that can't have a price put on it, is the number of smiles created by the RF when they make visits/host events/talk to people. I do think it is a shame when people undervalue their efforts, on many occasions because they pay no attention/have no knowledge of the work that goes on behind the scenes.
Of course, there are also the schemes that have impacted the lives of so many people - The Prince's Trust/Duke of Edinburgh - which have relied on time and inspiration, rather than just cash.
I'm obviously a royalist, and fortunately the majority of UK citizens are currently. I do respect the views of those who aren't, even if I don't like the aggressive way they go about stating them at times!