A totally enclosed 6 board box with mitered edges will blow itself apart in time - even if all the boards are the same wood. Mix woods and it gets worse.
BUT - if the box is made out of ply - with lock mitered corners, and then veneered - the veneer may split but the box will stay together and closed. Getting the right mitered profile on the right edges is fun but it is do-able - see
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make two versions of the lock miter bit, one for 1/2" and another for 3/4".
charlie b