That's true. But its best to replace them when their timings drop significantly, because a very weak battery is a headache and nobody likes to charge it 5-10 times a day!
Safety risk is there, worn out batteries are swelled and overheat above critical temperatures sometimes, as i monitor these things very carefully. Li ion batteries almost never explodes, when it does explodes, its a bit massive. It happens very rare though.
They suggest that primarily to meet safety standards and secondarily to earn profits. Most good brands phones monitor CPU and battery temperature all the time and they slow or even turn off the device itself when the battery or CPU overheats. So there is safety risk involved.
Those phones were quality stuff and lasted ages, newer models are not the same quality as those previous ones.