I began running saws a lot in 1977 (tender age of 15 years old) I've been wearing chaps since I knew there was such a thing, since about 1980 or 81, whenever I run a saw. I've never cut my chaps but I've seen several very experienced, proficient cutters slice their chaps open. One guy jammed so much kevlar into the tip of his bar we never could get it to spin again.
I always tell people chaps are like a woods lifestyle aid. On a cold day, you can slip your hands behind your chaps to warm them up, less of a commitment than putting your hands in your pockets. In the marginally cool weather we get in Northern Cal, they make a sort of bridge between wearing long johns and not needing them.
While holding a non-running saw, you can rest the saw on your chap protected thigh and keep your pants clean and experience less arm strain (lazy, I know). You can kneel down and not worry as much about rocks under your knee with chaps on. At lunch you can take them off, fold them up and sit on them and keep your backside warm and dry. Of course, you can wrap them around a bar to pad your shoulder for carrying a longer saw in or out of the woods.