I have used plastic tees for years without any problem. I worry even less when the tee box is very soft. Some golf courses do not like them as they can be harder on the mower blades but I always pick mine up and dispose of broken ones in the trash. I still occasionally use wood too. I just like to tee my driver high and most wood ones I have are a little shorter. I have some now that are 3 1/4" which work for me. The way I see it, the golf ball is plastic too. I don't think the tee will create any more stress on the face than hitting some of those cheap range balls. :)

Dale brings up a good point. Pick up your trash. The course maintenance will appreciate it. I'm a bit anal about it, but if I'm waiting on the tee box, I often will gather the broken tees and put them by the tee markers just to tidy up a bit.