Yes, private trees are an old sore spot for many of us. ;)
Note that some people don't have trees because they are adopted. (Not all of the people without trees, of course, but some, and maybe even a significant number. I have so many adopted matches at the other testing companies that I wouldn't be surprised if I have 100s of adoptees among my matches here.)
At the other extreme, some people are just cray-cray. A close cousin of my father's not only made his tree private but disconnected it from his DNA results... and he's someone who's savvy enough to be on GEDmatch.com. WTH, as they say. I'm just grateful that I got to see the tree before this happened.
By the way, when you delete the private or no-tree matches, they don't really go away. You can un-delete them at any time. I used to periodically visit my deleted matches in their holding cell (tiny link at the bottom of each page of matches) to see if any were now public (happens fairly often), but Ancestry's search engine doesn't seem to include deleted matches, so I've been restoring them.
Be sure to use the feedback button to let Ancestry know that sharing with non-sharers bothers you. People have put forth all kinds of possible solutions for making both sides happy, so it's really something we need to pester Ancestry about. (Considering that we can see names of people in private trees in the regular site search, surely the DNA search and/or match list could be loosened up a little.)