Is service by third party mechanics really the dominant factor in creating lemons, and not design or manufacturing defects or abusive driving by previous owners?

One of the largest factors is probably a lack of servicing. By requiring all servicing to be done by Tesla (who presumably keep records) they eliminate the "yeah I had that service done but I lost the receipt" scenario: If Tesla says that they didn't service a car, the buyer knows that it wasn't serviced.

Which the seller can mitigate by either keeping their receipts or having Tesla service the car, so the reduction in resale value would only apply to sellers who didn't do that, and then it's their own loss.

Tesla can offer a stronger warranty if they know more about the cars' life. The car is full of sensors.

If they offer a stronger warranty they don't need to prevent service by third party mechanics, because nobody is going to pay a third party mechanic to do service the manufacturer would do for free under warranty.