Tooth doctor doesn't have the same ring as eye doctor
Saying eye doctor in a conversation feels normal. Saying tooth doctor feels like listening to someone who had a bad disco elysium roll and they're punching themselves in the face to get the words out.
Technically a general eye doctor would be an opthalmologist. An optician is someone who makes lenses. The person you see for an eye test at the opticians is an optometrist (someone who measures what strength lenses you need).