Indeed. You get that and so much more useful information for free in your web-server logfiles. Any half-decent web server log analyzer tool will classify and graph all the useful data in those log files and present it to you in a nice shiny web page or report document of some sort. No cookies required.
Google Analytics doesn't use any third-party cookies; it uses first-party cookies only. [EDIT: this is too broad; see comments below] While the JS is loaded from a third-party origin, its notion of identity is entirely per-site.
It seems certain features are restricted to third-party cookies: https://developers.google.com/analytics/devguides/collection.... In practice though, moving from third-party to first-party is simply a way to reduce the probability that the spyware gets blocked by the user agent.
> certain features are restricted to third-party cookies
You're talking about the https://developers.google.com/analytics/devguides/collection... section, right? That's only for sites that are already using third-party cookies for advertising, has to be specifically enabled, and doesn't seem very applicable to our "know how many people visited my website" discussion? But my comment above was too broad, and I've edited it to point here.
> moving from third-party to first-party
GA, back to the Urchin days, has always been built around first-party cookies though.
I think so? It's about linking advertising activity (keyed by third party advertising cookies) with analytics activity (keyed by first party analytics cookies)
You can do that easily without third-party tracking cookies.