You are dead on ! I've seen this pandemonium before and have elected to avoid it altogether rather than wade into the fracus. And the corrective action suggested is clearly a do-able way of solving the problem.
Of course, getting any store to do that mean they gotta give a crap. I've tried similar things in other arenas of concern and found that few people that possess the logic required to see this problem and design a solution actually run a business. Their focus seems to always be in a hundred other places. But with enough care and nurturing it could be accomplished ... though I'd bet once "the help" cleaned it up they'd put it back the way it had been for years unless there was some cut-outs in the counter or marks indicating where everything was suppose to go. After all, it is hard to get good help.
Sure you could make your own coffee at home.... and I do sometimes. But this problem exists everywhere I've ever been to one degree or another. And I always figured these people just scheduled 20 minutes in the daily routine to execute a task that should only take3 if you have to wait in line to pay !
Oh ...and love the visual aids too !