Do any performance-focused vehicles use CVT?
Answer: No.
Answer: No.
"Ferrari has emphatically ruled out offering a manual gearbox in its next generation of vehicles, for one simple reason: performance. Speaking at the Frankfurt motor show this week, stakeholders at Ferrari said the manual transmission had become obsolete in a performance sense because modern dual-clutch transmissions were much faster and effective in their shifts."
"We never say no, but today we say no," a spokesman said. "We are very convinced with our strategy about the automatic gearbox, it's the fastest gearbox in the market and this is a distinctive component for us. Right now we are not thinking about a manual because the performance is [less]."
Not a CVT, but a manual has no benefit. Either go CVT for efficiency or geared automatic for performance.
EDIT: astrodust: Let not split hairs; Formula 1 allowed the introduction of CVTs in 1993 and then banned them because they were too good.
https://www.youtube.com/watch?v=x3UpBKXMRto
http://jalopnik.com/http-youtu-be-x3upbkxmrto-one-that-goes-...
They've had paddle-driven shifting on their cars for over a decade now which just triggers gear shifts manually. It's not an automatic transmission in the classic sense, there are still gears. Classic automatic transmission systems use a fluid mechanism to transmit power which is where a lot of the power loss comes from.
I assume you're talking about the paddle-shifted transmissions found Ferraris, Lamborghinis, BMWs etc. in the recent past. These in fact are the opposite of 'clutchless'. They were basically manual transmissions electronically controlled and with the clutch and shifting actuated by hydraulics.
Nowadays they use some variety of dual-clutch transmission.
It is odd to see in action; accelerating from a stop using launch control causes the car to not simulate gear shifts for maximum performance; the engine quickly climbs to about 6700 and just hangs there while the speed increases. No shifting drama at all. Almost boring.