I do not think alexa has much importance it depends upon where the users visited with the browser with alexa l
I don't agree with you, alexa rank is important for the site. You can see that how much your site will be important for alexa.com. Some peoples thought that it is useless, but it can't as per my opinion.
Yes I agree, I find it irrelevant too (these days). I used to believe that it has something to do with real traffic, something useful for your website but now I think it's no longer helpful (just my thoughts).