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... :)