It doesn't revise the fact that the film didn't really cue us into this explanation (especially with Sadness around who was often pointing out the shortcoming in Joy's plans), but Pete Docter was asked about this and had this response.
Okay, I do have to ask one thing. When it came to the core memories, why didn't she just push those through the hole and send them back up to headquarters the way they were doing with that commercial they kept throwing on a loop?
PD: Ah ha! We discussed that along the way and it was one of those things where we kind of boxed ourselves in a corner a little bit. We added the recall thing later, when they were doing the song that got stuck in her head. Our argument was that Joy wouldn't trust the memories would be fine on their own, she needed to be up there too.
Yeah, I was watching and just thinking to myself well she should just toss those things in there too and be done with it.
PD: Yeah, well then we wouldn't have a third act. [laughing]