Deprecated Social Proof
Back in time users didn't have any accessible indicator of the popularity of a page, "SEO" didn't exist. Social networks didn't exist. Users had not a clear way to determine the popularity of a website.
Someone could see a 3500 users visits indicator and think "oh pretty good!", because there wasn't a number or scale that users could think of as a reference to get an accurate idea of the popularity of the website they were visiting, even more if they acknowledged that the indicator could be "cheatable" so it wasn't something in which everybody could trust.
It was just an available indicator in that time, so people used it. Same happened with music auto-play. But why?
So, the indicator was there, a lot of people were using it, you didn't have as many ideas of what to add to your website to make it better, you had some "decent" numbers of visitors, and you liked to watch how the numbers went up, so having the visit indicator seemed to be better than not having it.
The Present
Nowadays, the things have changed. Internet numbers have grown enormously both in users and content, so for example a youtube video can have 5.000.000 views, a facebook post 400.000 shares, the number of users of an Android/iOS app could be millions.
Today there are more sophisticated, trustable and complementary indicators that serve as social proofs: likes, shares, comments, rewiews, SEO positioning, numbers of users using the app / downloaded it/ joined recently, etc. Of course, you still can "cheat" on some (bots, false profiles, etc), but if all your indicators are not consistent, people will sooner or later find out.
You can get to visit a page who tells how to cure a flu by eating a mix of apples and cat hair just because you click on a link your uncle has sent you, thus increasing the numbers of visitors of the page, but this does not give anyone a single clue about what's the value of that page for you.
You could just being rickRolled without even liking the song!
Additionally, they are not useful anymore to websites owners who now have advance analytic tools to track their site's visitors and much more traffic-related information.
In plain words: it has lost the perceived value it could have as a popularity indicator, and it has been replaced with more credible, modern, complementary and meaningful ones.