I just want to say YES to your idea to go cold-turkey on the diapers and go straight to underwear. IT WORKS! I did it with my son right at three, he also had no interest in using the potty, and he was trained in less than a week. Your son will not like having accidents, and will likely begin using the toilet VERY quickly out of necessity. When I took the diapers away (I prepared him that it was coming, counting down the days for about a week, talking excitedly about how he was a big boy now, didn't need diapers anymore, and mommy was going to teach him to use the big boy potty just like mommy and daddy and most of his friends!) I combined it with some of the ideas in the Potty Training in a Day book. Also DO NOT use diapers at night, move to pullups to reinforce the idea that he is a big boy and doesn't wear diapers at all anymore. Just take the diapers away, give them to a friend or something. We treat Pullups just like underwear and expect that they will not get wet at night. And 99% of the time they don't. We're still on the same package that we started using 2 months ago.
I don't think we can expect kids to figure this out on their own, rather it's our responsibility as the parent to "push them out of the nest" so to speak, especially on this topic. Look at it as a training issue, not a developmental issue that you just wait for him to develop. You wouldn't wait for him to teach himself to read, would you?
Good luck, it's a big step, and a big risk for you, but SO worth it, and you won't belive how proud of himself he'll be. It's really wonderful to see, and that's what parenting is ultimately all about, not teaching kids to rely on and maintain dependence on us, but to gradually give them the skills and confidence to navigate the world themselves.