The problem is never dealing with the things you have to do today -- It's dealing with the things you don't. Whether it's things you need to do sometime in the future, or things that you may never need to do at all, or the things that you want to do.
For me, keeping track of the three things I'm doing today is far less of a problem than making the decision what those things are, and in being able to file things away so I can say to myself (and to others), "If it's important, I'll deal with it (and won't forget that it exists), but for now it's not my top priority".
The point I was trying to make is that, over the course of the day, things come up. Most of them I don't need to deal with now, I might need to deal with them in the future, but I don't want the cognitive load of worrying about remembering them while I'm trying to do other things. Hence, I write them down. Maybe "thing #1" of my three things some days is "figure out what the other two things for today" should be, but it's nice to have some sort of bucket to dump thoughts into for processing later. Call it a remembrall, or a todo list, but it's silly to pretend it doesn't exist.
For me, keeping track of the three things I'm doing today is far less of a problem than making the decision what those things are, and in being able to file things away so I can say to myself (and to others), "If it's important, I'll deal with it (and won't forget that it exists), but for now it's not my top priority".