Update: I've removed all analytics. Turns out I didn't really need to know how many visitors I had.
I use GoatCounter to count visitors. No fancy analytics, no tracking, and no cookies. Simple to integrate, easy to use dashboard, and an open source solution.
It creates a server-side hash using site-id, user-agent, IP and a salt. The salt is rotated every 4 hours. This reduces the accuracy, but is sufficient to track a browsing session. The server-side hash is not persisted on disk and is permanently deleted after 8 hours.