I would ake the time to lower the ledge to the same as the counter and it looks like there is a piece broken off on one corner, not sure,I think the whole space looks cluttered so maybe a dcluttering of the rest of the space will lead to less mess there.Sometimes it's just a habit forming to put things away if they have a space so maybe just better storage would be the answer.

You can paint just the back of the bar & around the end side (going into the kitchen) with a high gloss or semi gloss paint. Dispaly some cookie jars or teapots in a collection along the top so there is no room to add 'junk'. Place two little post-it notes with 'Do not Disturb' at each end as a reminder for all the ADULTS not to place 'stuff' on the counter.