People say that about wood in the dishwasher, and it's true it does take a toll, but in my experience even cheap wooden spoons/handles will take hundreds of washings to really splinter. Most of my stuff is cheap so I go for it anyhow. I've probably only thrown out like 3-4 wooden items in 25 years, due to dishwasher wear.

Seems like with it being wooden/porous, the extra heat and sterilization aspect makes it worth doing (in addition to the convenience)