Being a fairly recent convert to tubular tires, I wonder why they aren't more popular? The only disadvantage I can see is that they require more work for initial installation. After that, I feel that they are less work.
I currently have three wheelsets, all tubular. Two sets are basically the same, Mavic Reflex rims with bladed spokes and Campy hubs. One pair have Continental GP4000RS, the other pair have Tufo S33 Special (21mm). The third set is a Neuvation C50 with Tufo Elite Ride 23 tires.
I first tried tubulars when I got a good deal on a wheelset from craigslist. My initial idea was to just buy the wheels for the hubs (it was still a good price for a set of campy hubs) but when I saw that the rims were basically brand new I decided to get a set of tubular tires and try them out. Since it was winter, I started out with a pair of wide Tufo Elite Ride 25.
I got a little over 1000 miles before the rear tire blew up. It was definitely on it's last legs anyways as the under-layer was starting to show through the tread. During that time I only had one flat, and even that one was not a problem, I was inspecting the tires during routine maintenance and noticed a big chunk of embedded glass. I pried it out and sure enough, pssssssst. Since I had pre-loaded some Stan's Sealant, I just rotated the tire so that the wound was on the bottom and Stan did it's job. I never had any other flats, nor did the existing hole ever re-open.
For the Lewis & Clark Ultra, I tried a new pair of Conti GP4000RS on my new wheels (the second pair of Mavic Reflex rims). I got a flat in the rear tire but it only took less than four minutes to fix the flat. The only way it could have been fixed quicker is if I had a support vehicle following me with a spare wheel. But this wasn't the Tour de France and I'm not Lance, so no support car for me...
Why are clinchers perceived as superior to tubulars? The cost advantage of being able to repair/replace the tube while still keeping the tire. In my experience, products like Stan's Sealant have negated this advantage.
The one time I had to replace the tire it wasn't a big deal either. I just pulled the current tire off and installed the new one, slammed the CO2 inflater on, and was on my way.
There's a trick to removing a tubular tire which makes it quite easy. I'll be doing a separate post on that with some video but basically the idea is to work a tire iron or screwdriver in between the tire and rim and then use that to pull the tire UP and away from the rim as you work the tool around the wheel. This breaks the glue bond and then you can just pull the tire off.
If I was doing a long tour or adventure ride I would certainly have to go with a clincher. It's also kind of a drag to carry an entire tire around. I haven't gotten the hang of a compact fold, so I just kind of wad the tire up and use a velcro strap to compress it so that it fits in a jersey pocket.
I think the reason tubulars aren't more popular is due to the perceived hassle of installation. They do need to be pre-stretched, rims need to be cleaned, glue applied and allowed to dry, then reapplied and install the tire. But so far I find the routine involved to be soothing, and it gives me a sense of connectedness with all the old-school riders that I admire and envy.