Brief recap: I see one of my main roles as a parent being building independence:

I want to let my kids be as independent as possible, as early as possible. Not only does it make their lives better, because they can meet their own needs how they want, but it makes my life easier, because they can handle more on their own. Sometimes this involves a bit more effort up front, but I think it's substantially less effort in total.

For a while I had an approach which was essentially, "if you can do it yourself I'm not going to do it for you." For example, soon after Lily learned how to get her own cereal, we had some conversations like:

Lily: Papa, can I have some cereal?

Me: You know how to do that!

Lily: I don't want to, and you used to get it for me.

Me: Now that you can do it I'm not going to do it for you.

Lily: [unhappy]

After a few weeks I realized this was counterproductive. Yes, it did mean more practice at new skills, and it is where I want us to end up eventually, but the incentives are all wrong. Instead of her former excitement at learning new things and expanding what she was capable of, each new skill now made her life harder because I was less helpful. You can sort of think of this as too high a marginal tax rate: I was claiming too much of the surplus from her investments in her abilities.

After I realized it wasn't working I toned this down a lot. I will still sometimes refuse to do things they know how to do themselves, but most of the time they're happy enough to do the thing on their own, whenever they want, at their own speed, and in they way they prefer, that I don't need to push them along.

One place where I'll still consistently refuse is when I wouldn't have done it for them even before they learned how. For example, if they don't like dinner and ask me to heat up something else I'll do that, but then if they don't like that I won't just keep getting them additional things. Now that she can use the microwave, however, Lily has an additional option, which is that she can go heat herself something up on her own.