Alexa is not super accurate for low traffic sites - those in the 250K and up range. They get their numbers from a variety of sources, including user generated and owner generated data. While much of their algorithm and data collection is a company secret, multiple visits in the same 24 hour period from the same IP are only counted as one visit.
What you may be missing is the usefulness of Alexa in a more general sense. I don't really care what the exact number of visitors might be to a website - those numbers are going to vary depending on the algorithms and programs used by various reporting agencies and apps. What is useful to me, as a content provider, is to find sites where I can put my content and expect a decent number of eyeballs to see it and respond to it. Thus, I have to combine both the "how popular is this site according to Alexa" with "what did the visitors use to find this site" metrics. If the visitors are using keyterms that I want to rank for, on a site that accepts guest blog posts or comments, that itself is reasonably popular, I'm going to hit that site to leave a comment, ask for a guest post slot, or ask for inclusion on their resource page. In otehr words, Alexa cuts my research time waaaaaay down when I'm looking for those all important backlinks from sites that are good for me.
That doesn't mean I'll do well with that site. That requires for real trial and error, but Alexa gives me a head start on that process and saves me a ton of time. But I have to use far more than just a raw popularity number in that decision and Alexa gives me the other things I'm looking for to help make that decision - where the visitors to that site are coming from, where they live or at least use the net, what terms they are using to find that site, and other similar sites that I can check out that could be even better for my purposes than that one.
I often enter my search term or phrase in Google to see who pops up, and then my next stop is Alexa to see how well each of those sites on the first page or two perform vs each other. Which is fastest, which has the most visitors coming from Google or YouTube or is there an upstream site that I've overlooked that might not be on the first page for that term but which sends a lot of visitors. So I use Alexa to help me build a skeleton profile of other websites, both my competitors, and those sites I might want to form an alliance with. And for that sort of info, Alexa is IMO unbeatable among free tools.