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A top lid might make it easier to reach in and grab things but how often does one have to go in this seat for things. Unless it is a straight window one and you can find a Hope Chest or kids Toy Box the right height and length.
In most cases they are built to match the color of the cabinetry already in the house but other times they are made to match the color of the furniture. With the front doors you can custom make a nice cushion on top in one piece is one good reason.

Either MDF or PB can be covered in laminate, therofoil, wood veneer or some other form of vinyl.
I'm just concerned about the materia, since my home style is very contemporary with no wood. Besides, many I have built these seats for end up putting a custom made cushion on top which would render the hinge useless anyway.
Contemporary style uses these materials but lovers of contemporary style never complain about PB or MDF like lovers of traditional do. If I wanted the unit angled like an octagon type shape instead of square it would be an add'l $250.

And second when you sit on the seat you feel the hump of the hinge on your caboose leaving an uncomfortable seat.

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