(I use it "web analytics" on my own site thus I can confirm that it's free.)
Is that what you’re using? Or did I misread their offering (which seemed to clearly indicate a paid plan was required for the non-JavaScript analytics)?
See at the bottom how it says “sign up for a paid plan” in the section that says “there is no code to add”:
https://www.cloudflare.com/web-analytics/
Edit: Oh, you're the OP! Just checked out your site and you are indeed using their JavaScript beacon. I know I'm being unreasonable, but in my case, I'm going for no JavaScript, and no trackers (so some sort of request logging on the server or proxy side is likely my only option). It's my attempt to "be the change you want to see in the world".
With regard to no-JavaScript sites I understand; and for example the only JS on my site is the one for GoatCounter and Cloudflare web-analytics. GoatCounter does fallback nicely in case of no-JavaScript, meanwhile Cloudflare just doesn't work.
However, with regard to Cloudflare web-analytics, given that I already serve my site through them, there is no privacy lost by also using their analytics.
GoatCounter is good for assessing a long-term picture regarding readership, meanwhile CloudFlare is good for assessing performance issues.
Also note that if one registers a domain with Google for their webmaster tools (previously called Search Console?), although one doesn't use any of the Google services on the site, just because your visitors are using Chrome you can get performance metrics that way... So that's that about privacy... :)