How much do you usually pay for a full mouth cleaning with an anesthetic and scaling? Does your dentist also quote a price with extractions included? If they talk about extractions are they more likely to want to do them? Can an owner tell by inspection in advance if a tooth needs to come out?
There's no rhyme or reason to dental cleaning pricing. I've seen discount clinics advertise $200 without xrays, and known people to pay $500. A few years ago, I paid my regular vet (generalist) about $300 dollars for a 50 pound dog, without any discounts--they have to do bloodwork for anesthesia if none has been done withing 30 days, so I can save about $100 next time by scheduling a dental cleaning within a month of my dog's annual check-up, so that we can re-use the annual bloodwork. (My vet included xrays in that price.)
My kibble-fed dogs need cleanings about every 3-ish years so long as they're chewing trachea tubes, bully sticks, and an occasional frozen chicken thigh. We can tell when it's coming due by looking at the tartar buld-up on the back molars. I've never had one of mine need an extraction during a cleaning (we've had some tooth injuries that we dealt with separately at a vet dentist though). FWIW, little dogs seem to need them far more frequently (and some breeds of little dogs just seem to have rampant tooth issues genetically).
A vet dentist would usually charge far more for a cleaning than a generalist. However, I've had very cheap cleanings added on to other dental work at the vet dentist (e.g., if they're already going in for a root canal for a damaged tooth, if I add on a dental cleaning it's something like $100 more -- that's 100% worth doing if a dog would need a cleaning in the next year or so anyway).
I don't believe that you can necessarily
look at a tooth and rule out all problems visually. When you go for a teeth cleaning yourself, they take xrays to spot cavities and other damage to your teeth -- the vet may use xrays the same way. They also may find stuff by probing during the cleaning. Theyr'e also carefully inspecting the inside of the mouth for other things (including oral cancer), which isn't usually possible during a regular exam.