What a brilliant idea. Must share this idea from a Blog named: Unclutterer. Unclutterer is the blog about getting and staying organized. “A place for everything, and everything in its place” is it’s gospel.
In the interest of safety, I would want the opening from the top, a hinged flip top stair lid. If one wanted these drawers as shown here, be sure to think in terms of safety. I would specify magnetic catches, or earthquake latches to prevent a drawer from opening forward on its own and tripping the unsuspecting user. With many stairs equipped with center stingers, a single drawer may not be an option but two drawers can be installed in place of one. This would be great for retrofitting the last two stairs.