^ here, here. Even with brakes, or even a road bike, a broken chain can cause serious injury. Depending on mileage and the road/weather conditions, I replace my chains 1 or 2 times per season. And that isn't even for safety: the chain is cheaper than the rest of the drivetrain and you only need to see what a worn chain can do to the chainring to understand. When I worked in the shop, I'd see rings that looked like sawblades the wear was so uneven...
chain = $
ring = $$$
chain = hard
ring = soft