Toddlers in general have very hard and fast rules about how life should be. They think very concretely, and see life in a fixed way. I think actually this is the best time to teach them to clean up after themselves.
During that point in life when things need to be a certain way to make sense, when they expect routine and expect that something that is there now will always be there, it’s a great time actually to teach them to clean up their own messes.
It takes repetition and time, but my son at any rate has responded well to this idea of necessary order and does a good job of cleaning up his room each night, wiping down his place at the table after meals and putting his toys in the playroom back into the boxes they came from. The big key in that though is that kids actually get distressed over too much chaos. A sense of order gives them a sense of reason. It calms him.
Disorder, to a lot of personalities can be distracting and troubling. It bothers me when I can’t find something I am looking for, just as it frustrates my son when he is missing one piece of a puzzle or one important part of a toy set. It also teaches kids responsibility for themselves and gives them a sense of control in a world that they soon learn is out of their control most of the time.
We sometimes give kids less credit than they deserve and underestimate their abilities to pick up after themselves and clean up the messes they have made. I am not super strict about it, but I do have my son clean his room before nap time and bedtime, put the toys back that he takes out in the family room before the end of the day and put all his bath toys back where they belong when he is done with a bath. If he finishes playing with a toy, I usually encourage him to put it back so he doesn’t lose the pieces.
He can do all of this at two. It takes just a couple minutes and gives him a greater sense of stability. Toddlers respond well when things are consistent. They need that developmentally. Sometimes when they are distressed, introducing a bit of order into their routines will help them to calm down.