A cutting board that is too thin has a much greater chance of warping or breaking.  At Stags End our end grain cutting boards are all 1 3/4 inches thick. This produces a very strong and durable cutting board without being excessively heavy to handle.  Thin cutting boards are not, in our opinion, durable enough to allow for the preparation of meats or vegetables with a sharp knife.
If you are purchasing an edge grain charcuterie board you can accept a thinner board as a charcuterie board is usually for displaying cheeses and lunch meats.