I don't actually follow anyone on twitter. I just got to three or four specific pages to see what content they've posted. Usually they share an interesting selection of tweets, which gets me exposure to more than just those specific people.
I don't really understand what the purpose of following someone is
What you're describing just sounds like a more labor-intensive method of following those people. The purpose of following people is so you can see that same content aggregated into a feed.
It has both modes. At the top of your feed, there's an icon that looks like three sparkles. If you click it, you can set your feed to "Home" (the Facebook-ish option where an algorithm creates your feed) or "Latest Tweets" (the linear timeline).
I don't really understand what the purpose of following someone is