We were not born with patience. Another way to get latex paint out is with ammonia. A 1 part household ammonia to 5 parts water will get latex paint off most substrates. I would check that on a carpet though because of the many chemical varieties that carpets are made from. This works on water based paint only. For kid's watercolor, your way is great.
Here's a tip for when the next step happens, crayons on walls or about anything else. Spray WD-40 on the crayon marks. It's enough of a wax solvent to remove the crayon and doesn't bother latex paint. When I do this, I ALWAYS hear "But look at that big spot on the wall. We are going to have to repaint." Give it a day or 2 and it will go away. If you need the walls perfect before that, use the mild dishwashing soap or handsoap and water that you talked about.