It would seem it functions effectively for a lid. Likely the expansion and contraction don't matter for that use. And/or, when needed one can set it on it's edge, boards parallel to the ground and give it a couple good whacks to set all the boards tight again.The connections (pegs, dovetails) don't attempt to make the lid air tight or
water proof - unneeded.
A cutting board built like that would probably function for a while, but the "open" nature of the joins between boards would allow "stuff" to enter the joints and that would allow growth of various things in the cracks. This type construction, because of it's permeability, doesn't seem best for cutting boards.
A cutting board surface needs, amoung other things, to be non-permeable, in both micro and macro spheres. Thus the joins are much more demanding due to wood movement. Probably there are ways to deal with this Maybe in the way of wooden wagon wheels with a metal band around them? And/or: What was the "science" behind European cutting boards built with the end grain as a working surface?
Regards,
Rufus