The real reason that strength training is so important is not just to get strong - although that matters hugely. It is to improve your balance and coordination. The way that works is interesting.
When you lift heavy weights, you send signals to your body to strengthen the amazing wiring system that a) tells you where you are in space (proprioception) and b) regulates the thousands of subtle messages that handle your coordinated response to stimuli.
You strengthen the signaling system when you use weights....you send strong signals over it and that renews and makes more subtle and effective the existing system. Your coordination gets better. Amazing but true.
It is partly a matter of tightening the fan belts correctly. A car has just one fan belt...you have hundreds. And they are constantly being tightened and loosened...so they will be perfectly set to do the particular task at hand.
When you get old - if you do not do weight training - the system of fan belts gets sloppy. Alignments are off a bit for this and that. And so you pull wrong and get hurt. Doing weights keeps the system of fan belt-tightening young and effective. So don't be a dope: DO WEIGHTS!