Hi Tim, Thanks for your lengthy response.
True that age doesn't matter, but your place on the family tree does - Given that the amount of DNA decreases per generation those from previous generations (parents, grandparents etc) are likely to match with more of your fourth/fifth etc cousins than you as they will have a larger sample to match the DNA from. 'Jorghes', above has a grandmother with 985 close matches, almost certainly because her DNA sample is larger to start with and matches further down some of her tree branches.
And yes, the number of "K" will increase as you build your family tree, if your branch then extends to the tree of a DNA cousin who has a 'brick wall' on their side of the branch.
My wife had two DNA close cousins whose trees 'ended' at "Henry Cassell" and his wife"Elizabeth Dickerson" - My wife's tree does not have either of these. Research showed that "Henry Cassell" was actually "Henry Cattle" and the son of my wife's 2nd Gt Uncle. He had married bigamously (using the same names and occupations for himself and his father, and signing with the same handwriting). Having contacted the descendants of Henry Cassell they changed their trees and my wife's number of Common Ancestors increased. We have also identified a significant number of her DNA relatives who would be linked with her as Common Ancestors if they put more people in their trees, linked their unlinked trees, or even had a tree at all. So yes you can increase K with effort rather than more cousins taking tests. Slightly more than half of Tricia's close cousins with common ancestors were gained through changes to her tree, the biggest when she discovered that her grandfather was born Benjamin Hubbard, not Benjamin Herbert (changed his name on joining the army at 18).
I note that you added your 'more close cousins' to the Private Linked tree" value. Was this for a reason? but yes, I agree with your figures