I like this better than the underbed box. I might see about doing this and keeping it in the family room tucked into a corner. It would be right there where DS plays, and eventually we're going to have much more lego.
How many legos do you have in each drawer? Do you divide them up within the drawer?
I'm going to give a try and see if DS can keep this up. He's surprised me by keeping his clothing drawers organized after I put dividers in the drawers, and he has no difficulty with putting his toys into different types of bins based on what they are - I think it helps that the toys bins are clear, so he can easily see.
I'll post back with updates.