I remember some time around mid-1990s when our school got their first computers, and we were learning how to use them. We were given some kind of task that involved inserting clip art objects into a document. As a young kid with little computer experience I found that task difficult. So I asked the teacher whether it's okay if I just print the clip art objects, cut them out of the paper with scissors, and glue them into the printed document. (Teacher didn't allow that, because that would've defeated the purpose of the exercise.)
Things that are second nature for us today weren't necessarily that straight-forward in the past. Children in the recent past may not have had easy access to PC, and they may have lacked typing skills too. So using pen and paper would've allowed them to get their report done faster.
However, the episode in OP's question aired in 2003. I think the joke might be a little bit dated at that time; a lot of people in my social circles did have their own PC around then. But they were usually family PCs, and you had to wait for your turn. And even back then most people I knew weren't very fast at typing, so pen+paper might've still been faster for them.