I had two beautiful 2” thick commercial wood cutting boards. I came home one day to find my wife had thrown them out and replaced them with plastic, “so the didn’t poison us.” I, not so politely nor quietly, explained that wood had a natural antibacterial quality to protect the tree. All you had to do was to keep the wood clean. Plastic didn’t have that protection and if the impregnated the plastic with poison it would make you sick. The microcuts in the plastic would harbour bacteria and is nearly impossible to wash out. A few years later the wife read the same information from a reliable source (in other words, not from me). The plastic magically disappeared and was replaced with cheap 1/2” thick cutting boards.
I my experience the splitting is due to improper alignment of the wood grains, a natural flaw in the wood, or other construction deficits. I made a wood chess board that has a crack that opens and closes as the dumidity changes. You might mix sawdust, of an appropriate color, with the glue of your choice, and fill the crack. Whatever you decide to do I would expect to experience another crack in the same area. You may be lucky, it doesn’t hurt to try.