Reasons why DNA participants have no trees or private trees:

#1 and the most important reason is they have a different reason for taking the test than you do.

Every single DNA participant has paid $99 to do as they see fit with their family heritage, even if that means just getting an ethnicity prediction and going no further. In fact, I would bet dollars to donuts that the vast majority of the 'no trees' have no desire to research their tree - they just want to know if they have that fabled Indian princess in their past. So, those folks are useless to you anyway. They've done no research and they have no intention of doing any.

Or...

They are not tech-savvy enough to use ancestry.com - they may have hard copy trees they can copy and send to you, or an online tree somewhere else. I've had this happen several times.
They had good intentions to become involved in genealogical research and life happened and their intentions were sidelined for more important things
They allowed someone else to test them under the condition that the their results would go no further than the person requesting the results

Then there are the private trees. I have several private trees that are not connected to DNA - YET. But one will be soon and it will remain private. Why? Because my dad was adopted and I am looking for his birth family. I have several research trees of my paternal matches, but no definite leads my dad's bio family yet. My brother and I am going to take another DNA test and attach the results to a massive, wildly INCORRECT and THEORETICAL tree to see if it generates any DNA Circles. It would be very, very wrong for me to make this tree public when there will be absolutely no accuracy to it.

How many private trees are research trees used by adoptees or folks who are aware of NPE shenanigans in their family? A recently found cousin of mine (same very uncommon surname as my mom's maiden name) had his tree private because he couldn't connect his gggrandfather to our very well researched and pre-Colonial line, so he was convinced that there was an NPE in there somewhere. He didn't want to screw up anyone else's research by putting out information he couldn't prove to be true.

Sometimes people make their trees private to protect yours.

Then there are the old school folks - the ones that traveled to the county seats and city halls and libraries, paid for photocopies and read microfiche until their eyes bled and they can't stand the thought of someone carelessly nicking their research and photos.

It's not so difficult to throw together a boilerplate inquiry email and paste into a private message to whomever's tree you want access to and be sure to include your email address so you can share files and communicate more freely than ancestry's poor excuse of a messaging system. Be kind, considerate and gracious. Most of the folks I have reached out to have responded. Some have more information than others. Some are more interested in help than others, too.

Keep in mind that not everyone checks into ancestry every day and it may be months before you get a reply. I used to get email alerts when I had a message at ancestry, but I don't anymore, and I just replied to messages from 2 weeks ago.

What kind of information about yourself do you choose to keep private that the someone else might want access to? Consider this before calling someone else 'selfish'.

Lastly, be patient. More people are testing everyday. Your pool can only continue to grow and as it does, more matches will have trees of varying quality that you'll have access to.