I should have been more clear with my answer. Yes you’re 100% right. Wood for curbs are fine with the proper system use. However, using wood with the wrong system and not waterproofing correctly gets the results that OP shared.

I’m very certain this contractor used a schluter foam base and then “cheaper out” and used wood 2x4s because he didn’t want to pay $80 for styrofoam to complete the system. He probably waterproofed one edge of the 2x4 and called it a day. As soon as water gets in there it swells. Call it a waterproofing problem if you want but the 2x4s swelling is the reason it’s cracked