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.
I think the 'easier to say' part is the key thing here. "Pee-dee-atrition" is a lot easier for most English speakers that "op-tha-mologist". I think the "th" throws people off enough to just say "eye doc"
It's even harder to spell than it is to say "ophthalmologist" What are the extra h and l doing there? I don't know. Most people forget them. Another English word not really pronounced like it's spelled. Trips me up every time I try to type it out. Optometrist, the non-MD eye doctor, much easier to say and spell.
In the US at least, an optician is specifically a vendor of eyeglasses. The person who measures your vision and gives you the prescription is usually an optometrist. Neither of the above are physicians; whereas an ophthalmologist is a physician who treats eye diseases.