on your road cars, they are not sequential gearboxes. They are glorified automatics with fancy paddles and gearlevers, but still tend to be ecu controlled.
A proper sequential gearbox is mechanically operated either with a gearlever or a hydraulic ram linked to paddles. It does not need a clutch per se. What you have is an ignition cut off to cut the power as you change gear and you push/pull that lever as fast as you possibly can to engage the (dog) lug gears.
There is usually a clutch to give mechanical sympathy and extend the gearbox life. Smashing the lug gears into position can chip them, eventually you start loosing gears so a clutch allows a more delicate gearchange. Best practise is to use it under braking when the downshift is not so time critical.
For my racecar we could potentially save a second a mile using a sequential gearbox over H pattern
Kev