The problem is with you definition of want. You’ve formulated it based on the conclusion you’ve wanted to reach - that there is no other reason to do things, not based on what you actually think it is. That’s why I asked for your definition - to try to find a counter example, without you moving the goalpost and saying that that’s actually a want as well.
Well, I neither have to nor have any strong desire to wake up early on a Saturday, but I still do because of a force of habit, how does that fit into your definition?