Lots of breeds have distinctive haircuts. I believe it is just for show, no reason other than to have a standard look.
Poodle
Schnauzer
Wire Fox Terrier
Bichon
Portuguese Water Dog
Shih Tzu
Wait, so why is the Bedlington haircut a thing? I know poodle cuts are supposed to be to protect their joints in cold water but that’s the only breed I’ve seen before with a distinctive/recognized haircut. What’s the reasoning for the Bedlington terrier?