If you don't use it, you don't need to carry it. Save your pockets for stuff you use regularly. If the only thing you use on a day to day basis is your phone, then that is your EDC. If you want to be trendy, call it your ultralight EDC.
If you carry something that you haven't used in a month, leave it at home, it's just "stuff." What you should carry every day differs by person, and can change as your life changes. You may have no need for knives or pliers in your daily life, so why carry them around?
I draw and write daily. On paper. With a pencil. It's what I like to do while waiting for appointments, on break at work, waiting for friends, etc. So, a pencil and notebook are EDC items for me. Someone who uses their cell phone for all their note-taking needs, and who has no interest in drawing doesn't need a pencil, pen, or notebook in their EDC. It would be a waste of space.
Granted, if you only carry your smart phone, and I have a pencil, I can gouge out zombies' eyes when the Apocalypse arrives. You'll have to bash their skulls repeatedly with your phone. Clearly, I'd have a tactical advantage. You'd have less weight in your pockets, so maybe you'd get speed and agility boosts. Things to consider.