A lot of my expectations about kids come from being an art teacher, long before I even had kids of my own. The 1000+ kids I saw each week for art classes were plenty at the time and I definitely had my own style for sure. Growing up art teachers were my favorite teachers in the entire school and some of them were definitely the stereotypical hippy types, but I loved them just the same. When I became a teacher I was much more strict about keeping our supplies in order, everyone cleaning up their own spaces, and being on time. I should've known I was destined to be a professional organizer even back then, but hindsight is 20/20 of course.
During my teaching years, the homeroom teachers would come to pick up their classes after art and find their entire class sitting at their tables, music playing, everything cleaned up, and ready to go. I set expectations the first day of class (repeating the procedure for each and every class for several weeks) and I expected nothing less.
The whining about cleaning up was shut down quickly with the explanation that this is a community space that many people use, so it's not fair to leave your mess for others.
The same rule applies in my house to this day. Popular variations are "leave it like you found it" or "what if the president stopped by unexpectedly for a visit?" or "you know where that belongs so put it in its correct home please."
There are lots of school rules that you can easily apply at home for your kids. They might even respond better to these rules since they do some of them throughout the day anyway - ever sing that school clean up song with your kids? It's just automatic at this point and it really works, so let's clean up, clean up, everybody, everywhere... (are you singing along with me?)
1. Teach them to clean up just like at school
Teachers often give a 5 minute warning because they live and die by the clock. Issue your 5 minute warning before transitioning to dinnertime, getting in the car, bedtime, or whatever. Use an auditory clue instead of increasing the volume of your voice. I've used music - you must be cleaned up completely before the song ends - or even wind chimes, which amazingly stop a kid in their tracks even though they are so quiet.
2. Label with words and pictures
This works to help with little kids who can't yet read and for those that respond better to pictures instead of words. Identa-Labels work well, paired with free printable toy labels from Pinterest to slide inside them.
3. Sort like with like
Whenever you feel inclined to just dump things in a box and be done with it, think of your kitchen cutlery drawer vs. your kitchen junk drawer. It's never hard to find a fork in anyone's home that I've been to, so make it that way with everything, especially toys. Miscellaneous is not a great category.
4. At birthdays and holidays get rid of the old to make room for the new
As new toys/art supplies/whatever comes in, get rid of the old and ratty. You can also sell or donate items instead of just throwing them away. In fact, schedule this purge one week before a birthday or holiday so the empty space is already there, waiting for the inevitable new items.
5. Schedule regular purges
As the seasons change, so do your needs. Christmas music in July is irritating to me and so are out of season toys taking up prime space. If it's past its prime, get rid of it. If it's still good, store it away in a labeled box to be taken out at a different time of the year. You don't keep your Christmas decor up all year do you?
6. Keep checking for age-appropriateness
Books especially tend to hang around long after they are useful. Donate items that are too babyish to a local school or have a garage sale.
7. Don't let them leave a mess for you
Going back to #1 - cleaning up is super important, especially if you want to raise children who handle things for themselves. Unless there is an emergency, always have the kids clean up when switching activities, leaving the house, or heading to bed. Returning to a clean space is much more peaceful than a dumping ground and it is really all about maintenance. If you know where everything goes, it truly does take just 5 minutes to whip a room into shape before leaving it.
I don't think the President will check for dust should he stop by, but he will definitely notice the Lego he just stepped on. Since lawsuits are never fun, teach your kids to clean up, clean up, everybody do your share.