As long as a driver has one wheel still inside the white line, he should be fine, right? So the tarmac run-off area may allow drivers to enter the corner slightly faster.
Of course a smooth tarmac run-off area is the safest possibility, but I don't really like tracks that do not punish drivers for their mistakes. So what about using different kinds of tarmac? A strip of very slippery tarmac just outside the corner to punish the drivers for exceeding the track limits and then progressively more grippy tarmac to slow down the cars in case of an accident would be safe and challenging.