If you are a hater of cookies, Matomo is able to run with no cookies. There is a setting in the user interface: cookies are easy to disable.*

But cookies are enabled by default. Why? The Matomo Visitor ID cookie is a first party cookie! Look it up: that's a respectful, ethical type of cookie.  And the data it collects goes to your website, only.  So if you are trying to keep a lot of secrets about what goes on in your website, Matomo is the way to do it. 

Matomo explicitly promises that they have no interest in your data. See these:
https://matomo.org/100-data-ownership/
https://matomo.org/matomo-cloud-privacy-policy/ (Matomo Cloud only)

How to see the Visitor ID, and confirm that Matomo sets a cookie during the visit:

1. Go to your website in a browser.
2. Open devtools >> Application/Storage/Cookies
3. pk_id is the visitor ID. Its value is a 16 char string.
4. Go to your Matomo dashboard.
5. You can see this 16 char string in Visitors >> Visits Log (see the screenshot above)

*What Matomo loses when you disable the Matomo cookie, is it cannot detect a returning visitor. This messes up some of the more subtle things you would want to know about your website. Returning visitors are a pretty big deal to understand.