Carleton, I will share my experience. In my first races on the track back in the early 90s I got to watch several riders flat clinchers and immediately roll the tires off causing major incidents. Seeing that will make you swear them off. A couple of years ago I built a set of clincher training wheels and had some unsettling experiences with them. When I would turn hard on the track it would feel like the tire was rolling off the rim. I switched back to tubulars and haven't looked back.
The above said I am larger than the normal track racer, and I tend to be hard on equipment. I have seen plenty of people ride/race on clinchers with no issues, but my initial experiences of having to dodge riders who crashed due to tires rolling off of clincher rims I won't ride them on the track.
Nate