I also dropped Google Analytics from my landing page. I just use Google Search Console for SEO and search engine traffic info, and my own tool, userTrack for on-page stats and UI/UX testing (userTrack is like FullStory but self-hosted and with slightly more Google Analytics-like features).
I think it is important to have key metrics to measure your success. This is the whole idea of the lean startup movement. Build, measure, learn.
The most important thing IMO is to pick the key metrics.