Yeah, I also wouldn't take stickers off a chart either - it really is supposed to be a positive tool.
I'm like Arcadia, I end up cleaning up with DD (who is 6!!!) because it's the only way it'll get done completely, and it really is her just wanting to do stuff with me. She is actually really enthusiastic once we get started even though she will (frustratingly I admit) refuse to do it by herself. Both my girls are like this, refuse to do an activity until I get them started, then they complete the task and often enjoy it.
And there's no way I'd throw our toys in the bin. It'd probably upset me more than them, lol.
I do totally KWYM about not always having the time to do it yourself. We are the same some days (my work days particularly). The result of all this is that our place tends to be messy a lot. I'm ok with that though, so I guess my philosophy wouldn't work for everyone