It sounds like you're producing high school math material, whereas I'm teaching mostly physics (and a little math) at a community college in California. Hopefully there is enough overlap to make my experience helpful to you.
I do a variety of paper and pencil exercises with my students, some of which could be characterized as worksheets. Below is an example of a typical exercise, which students would do together in small groups. Most of my students have the (free) book in PDF form only. Probably 25% buy the book in print. (It costs $12.) Quite a few are using the PDF on a phone, although I try to convince them not to do that. There are desktop computers in the room, but not enough that every student could sit at their own computer. Students cannot print from these computers.
Given this set of circumstances, I often do print out the exercises for my students. For the exercise below, for example, I would print out one copy per group, in order to encourage them all to focus on the activity together. I tell them to try to agree on what to write down on the paper. They also have it in their copy of the book if they want it later for reference or if they want to transcribe their own copy of their group's results. While they're working, I do laps around the room and look at what each group has agreed to write down. If they're wrong, I give them feedback. The work doesn't count toward their grade.
"structured writing on paper"
Yes. If I just popped up the figure on the screen and asked them to do this activity, without a form on paper for them to write on, they would scribble random, disorganized stuff, and I would have no way to check them and give them feedback.
"do not have to copy exercises from screen, print worksheet"
Yes. If I didn't push them to use a paper copy, many of them would be trying to do this off of the tiny screens on their smartphones, which would be ridiculous. If this was high school, then there would be the added issue that many schools don't want kids using their phones in class, so many kids do not have any digital device. There is also the theoretical issue that some kids might not have any device, but I don't encounter that at my school. (I actually don't own a cell phone myself, which my students consider a bizarre eccentricity.)