Yes, although there are ways to reduce it (perhaps in a way similar to POSTNET; this would reduce the space taken up but require more fill in at once). But you do not have to fill it in right away you can do so after the game is finish
Would you mind quickly explaining what you guys mean? Sorry, I'd love to improve it but I'm not sure I get it. If you had a bunch of bubbles for each square and piece etc. wouldn't you be taking up much more space than 5 boxes? And it's also a huge notation change for everyone