Although time trials have a place in racing, most racers do mass start races. In those weight and aero are most beneficial. The difference might be, for me, 10% difference in average power during a race. Since I'm not strong I need to hide from the wind and keep my efforts to a minimum. With my heavier aero clinchers I never finished a Tues Night race. At the same races, against basically the same guys, I was sprinting for the win on my lighter aero tubulars (one clip here, another here, among others). 10% effort in many of my races is the difference between not finishing and finishing, and in more marginal cases, the difference between only being able to finish and contesting the sprint at the end.

Also the aero tubulars are more aero than the clinchers, even though my rear clincher is 3 cm taller (9 cm vs 6 cm). This is because the tubulars I have are wider and have better aerodynamics. Although you can buy similar clinchers now back then it was only available in a tubular wheelset.

Finally a tubular tire, even if flat, offers some rideability. You have a very good chance of staying upright if you flat a front tubular while diving into a corner at 30 mph. There's no way to stay upright with a similar failure if it was a clincher. I've flatted a front tubular (when I was training on them), rode a mile or three, saw two guys doing a paceline on a major road crossing my path, turned onto the (slightly descending but still rolling) road, chased them for a couple miles at speeds between 25 and 35+ mph, and caught them, all on an absolutely flat front tire. I politely declined to pull through and explained that although I was okay crashing myself due to my flat front I wasn't okay taking out two guys who were towing me. We all slowed down because the two guys wanted to see the flat and asked me where I flatted, etc.

My red bike when it was orange. Training wheels on it. Aero training wheels to the right (one is sort of in the background, the other one is the wheel most to the right). Aero race wheels on the left.