I like the design…especially the open sides. Is the dust problem dust on the box itself or dust on the contents of the drawers? For dust in the drawers you could always take a soft cloth and lay over the top of the contents or make thin lids to cover it.
I like it open, very architectural and shows the contrasting woods to good effect. But I'm kinda of like Pigpen from Charlie Brown, with a perpetual dust cloud around me/ I probably wouldn't notice a difference…
I like the grain continuity across the shelves, and the joinery (or is it inlay?) detail on the top.
Nice sense of proportions. Sell this one and make another with enclosed sides. If you spend your time correcting all your mistakes on one box, you have one box. If you make a better box you have two to sell.