It depends on the accuracy and speed. If a dog can detect cancer in a stool sample with 90% accuracy, and the dog can go through 1k+ samples a day, then that sounds like a good deal. The value proposition is in high volume and low invasive tests that can reduce the need for slower or more invasive tests. If we could screen everyone for colon cancer from a stool sample with a trained dog, then we could reduce the recommended frequency for a colonoscopy and still catch as much or more cancer. There is a lot of money saved if the average person without colon cancer only needs 1-2 colonoscopies in a lifetime instead of 4-5.
If there were a machine that could only detect one disease, I don’t think that automatically precludes it from being cost effective. I could see a dermatologist buying a cheap pen-sized device that solely detects skin cancer, at least.
Maybe, but dogs (or any animal, really) require constant care in a way that machines don't, and need space and staff for boarding, exercise, veterinary care, etc.
(Unless somebody is working toward a cheap pen-sized dog...)
For better or worse, we already manage large numbers of cattle and chickens. For the most part we don't feel bad for them. Treating dogs in a similar fashion would probably not be socially acceptable. What does the use of diagnostic dogs look like at scale?