At 13 mos (& 25 lbs), my dd still spends a lot of time in her sling . I use it to nurse her and get her to sleep for naps and at night. I have tried other ways to get her to sleep - they have not worked for us, at all!
I also use it to do things around the house if she's fussy. She loves to be up at my level where she can really interact with me. I think it must be hard to be so tiny and have the world happening so far above you that you can't get in the game. The sling helps alleviate the frustration I think toddlers normally have when they are unable to see what's going on, much less be a part of it.
I also use it for short errands. It's much more convenient (quicker, less cumbersome) than a stroller or a shopping cart.
Another reason to use a sling with a toddler - they're heavy little buggers!
No matter what kind of parent you are (AP or not), you end up holding your toddler a lot. The sling takes the weight off your arms and puts it on your hip, allowing you to hold them even longer.
I would be lost without a sling, even now that my baby is a toddler.