For those who want a similar system but stay digital, you can use Things from Cultured Code. It has the concepts of Today, Someday, and Anytime.
The process for me is similar to OP: each morning I add tasks to my “Today” list, which can carry undone tasks from the previous day. If you complete the list, you can always add some more tasks.
You can also plan ahead and build a backlog of tasks to do, and just browse through them to add them to your “Today” list.
Simple system, with not many parts, but extendable with Projects, Notes, Repeatable tasks, Reminders… Also integrates with your calendar to keep everything in one place.
Very polished product that can be as simple or as complex as you want it to be (but mostly simple).
I initially balked at the high price of things but WOW I've never been so productive using it. And like the analog site says - it feels so good to cross something off.
I also use a similar process and its easy to backlog things that you know you just won't get to today. I recommend this app to all of my friends and +1 for the commenter above.
[0] https://github.com/alainm23/planner
[1] https://twitter.com/planner_todo/status/1492084099875586049