Back in the 60s I took the Evelyn Wood speed reading course. It works exactly as you describe. At first, one uses a side to side motion of the hand to pace the eye across the page. As one gets better, the page can be read with just a top to bottom motion. People who see you do it assume you are just skimming, but in fact you read every single word. It s a fantastic skill that I don’t use very much any more, but when I was teaching it came in very handy.
It was considered good if you could read 300 words a minute; the average was somewhere around 250. I maxed out the machine (at around 5,000 wpm, if I recall) and of course the teacher thought I was faking it. So she tested me on the content and I aced it. She couldn't believe it. But I proved it numerous times afterward, and not just to her but to other teachers as well.
It is reported that JFK could read up to 20,000 wpm.