There are many reasons, here are some of them:
Formula 1 cars generate up to 3.5g of force, which requires significant strength to be able to balance and focus through.
It can get very hot during a race, especially when in hotter climates. Drivers can lose up to 3kg of sweat during a single race
It takes strong neck and shoulder muscles to keep your head from whipping around as you go through corners, and powerful arm muscles are needed to keep your arms from getting weary after holding them on the wheel all race.
It also takes VERY strong leg muscles, as the cars are "brake by wire" and do not have traditional power-brakes as a modern road car does.
They say a formula 1 race is as much of a fitness challenge as running a marathon!
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Not Realy considering Rugby run more then the Formula One drivers, rugby players average 10 Km a session :S and why would drivers want to be fit
I suspect the answer is yes as rugby demands high level of physical strength, stamina to maintain the tackle and attack contacts and of course to play 80 plus minutes