I do worry about potential issues. If students can get more copies of handouts on their own, then what encourages them to keep track of the first version? When I was a student, I had to organize my papers and when I failed to be responsible, then I would have to face my teacher's disapproving expression. I wonder to what extent I'm enabling the students who could otherwise be organized.
The other issue is related to learning. The research is clear: students learn more effectively when they are writing on paper, rather than typing on a screen, and reading from paper than from a screen. The move to paperless is counter to the current data on memory and learning. I suppose the appropriate response is the sum total of human collective knowledge is readily accessible via mobile devices, at lighting fast speeds; therefore, education should shift from memorizing facts to higher order tasks - a fair response indeed. But I can't imagine these advocates would argue against students memorizing any facts. The question, rather, is how many facts ought to be memorized.
I tried this year to move back across the aisle to using paper. At the beginning of the year, I told students they had to print the video note sheets and hand write their notes. We also briefly talked about the research that supports this mandate. I also provided binders, free of cost, to students who wanted them. I have to admit that I haven't been enforcing this mandate. I have no idea how many students are taking handwritten notes. Guess it's time to find out.