Sounds like you want drawers added to replace the cubbies.

Yes, drawers would be great idea. Have you seen any examples of what this would look like? Thanks

It would look exactly like the drawers on the right

Okay, I'm worried about losing space. I think doors would be better

What about a drop down door ?

I think a door hinged at the bottom would be the most convenient to use. I know my family well enough to know that if it isn't REALLY convenient, the shoes are going to get left on the floor!

Will the storage get used if it has a door, drawer, or anything? Could they be kick-spring or motion activated?

You could try attaching the cover with magnets. You'd need a light cover, maybe opaque plexiglass. If you have the magnets in the right places, you could put 4 covers on, one for each kid. When I wanted my kids to do something and they didn't do it, I'd take a picture of the offense (ie shoes not in cubby) and assign a chore. Usually, it was related to the offense, like saying, "I couldn't vacuum because your shoes weren't put away, so please vacuum the mudroom." This worked well for dishes not in the dishwasher, as it was daily. Although, thanks to automatic cloud storage, somewhere, there are lots of pictures of dirty dished left on the table.