Other sports leagues have teams that ban their athletes from participating in dangerous recreational activities during the season (and some during the off-season), so it wouldn't be unprecedented for NASCAR teams to do the same. There's an inherent danger in daily life (such as driving your personal vehicle, which in Chase's case also includes flying). Still, teams try to minimize the risk by not letting their athletes do other risky activities when they're in season.
I'm not saying it's good or bad, but I've always found the laissez-faire approach to drivers to be a bit of an oddity, especially given how much rides on the success of the individual driver. If a ball sport player misses time, he has teammates who can pick up the slack, but a driver of Chase's caliber is more challenging to replace than even someone like Tom Brady.