I certainly don't stress over analytics, refreshing them frantically throughout the day, but it is useful to review them from time to time.
For example, when looking at the analytics for the Mastering Laravel site, I noticed someone was using Gumroad's global affiliate program to drive sales of our validation book, without ever talking to us.
After seeing this, I contacted them and offered them a much higher affiliate percentage, as we really appreciated their efforts.
Little insights like this make it worthwhile to pay attention to analytics.
Here to help,
Joel
P.S. Speaking of affiliate links, here's my link for Fathom Analytics, which is what we use for web analytics.