Introduction
Existing answers that discuss this rule mostly discuss about the effect of using a laptop or not on students. Therefore, I want to start by stating that, if the use of laptops affects the lecturer negatively, then it is arguably reasonable to enforce such a rule. Then, I will give an example of that situation in real world and describe how the rule had been enforced in that example to answer the poster's question.
As some other answers have pointed out, university students should be treated as adults. Therefore, even if not using laptops is truly beneficial to students, or in general, if there is some way to learn better, I believe a professor still should not force a student to use that way, because a student has freedom to choose how to learn. On the other hand, if using laptops can be proven to affect the professor's performance, which in turn affects all students who listen to his lecture, then that could be a good reason to ban laptops.
Example
I am not a professor, but I have experienced lectures of a professor who enforced a no-laptop rule there, and who arguably had good reasons. That is the example that I will give in my answer.
Last summer I was self-learning 6.034 Artificial Intelligence by Prof. Winston (R.I.P. Prof.) at MIT OpenCourseware. He published the recordings of his lectures, and in the first lecture where he did an introduction to the course, he emphasized that one of the class rules was no-laptop.
"..., and conclude with some of the covenants by which we run the course.
One of which is no laptops, please.
I'll explain why we have these covenants at the end."
Unfortunately, he probably had forgotten to explain why no laptop was allowed at the end of that lecture. Nevertheless, his gave his explanation elsewhere. But instead of directly going there, I want to sequentially narrate the events.
When I heard this rule, I was quite skeptical of the benefit of it. Partly because I didn't know the professor before, partly because I had been taking notes in a paperless way --- in classes I used to take notes by my keyboard attached tablet, on which I can both type in LaTeX and draw. Yet only after completing a few more of his lectures, I noticed they were really enjoyable, which meant they took great efforts to prepare and the prof. cared about his lectures and his students. So I was quite eager to know his reasons behind that laptop rule.
Throughout the whole course of 23 lectures, there were three times when he took action for some student(s) violating this rule.
Lecture 8, before starting, he was showing a program that was performing a task in a computationally impossibly way: "We're going to wait till either all the laptops are closed, or this program terminates, whichever comes first." He sounded quite firm from the recording, but he didn't actually pause the lecture for that. Because it is a recording, I don't know if the students obeyed or not.
Lecture 11, When he noticed an open laptop, probably. "Can you put that laptop away, please?" No further action. Also unclear if the student obeyed.
Lecture 14, "Could you close the laptop, please?" Same as in Lecture 11.
To conclude, he probably only took action when he noticed open laptops and only took action verbally. He fully explained this no-laptop rule instead at the start of his How to Speak talk.
"Now, in order to do that, we have to have a rule of engagement, and that is no laptops, no cell phones. So if you could close those, I'll start up as soon as you're done. Some people ask why that is a rule of engagement, and the answer is, we humans only have one language processor. And if your language processor is enga-- could you shut the laptop, please? If your language processor is engaged browsing the web or reading your email, you're distracted. And worse yet, you distract all of the people around you. Studies have shown that. And worse yet, if I see a open laptop somewhere back there or up here, it drives me nuts, and I do a worse job. And so that ensures that all of your friends who are paying attention don't get the performance that they came to have. So that's it for preamble. Let's get started."
He explained why the language processor he mentioned was important near the end in Lecture 19, by mentioning a series of experiments conducted in Harvard University (link to paper), which he remarked as "in my way of thinking, is the most important series of experiments ever done in cognitive psychology, developmental psychology, actually", and which basically demonstrated the language processor played a vital role in the difference between the intelligence (mostly spatial capabilities in that research) of a human adult and that of a child below 5 or a rat.
Conclusion
Putting all these together, Prof. Winston believed using a laptop in lectures could
- negatively affect the student, especially by jamming the student's "language processor"
- more importantly, distract surrounding students
- most importantly in his opinion, affect him as the professor, which implies all students would be affected.
And he had enforced such rules only verbally by
- Before the start of some lectures, warning that he would not start until laptops were gone, although he didn't actually seem to stop for that
- During some lectures, asking the student who he spotted to have opened a laptop to put that away.
, which may not have good effect on some students who regularly ignores your ban, but at least respects the students' freedom as adults. On the other hand, I believe you could use Prof. Winston's reasons to persuade these students.
As I have only been a student, I don't personally know if a professor's performance will really be affected by seeing a laptop. But I hope Prof. Winston's reasons and how he enforced the rule could help you.