My mother is obsessed with this! If you have a slightly trailing lace you must sort it out straight away lest it trip you up and break every bone in your body.
I have never, in almost 45 years on this planet, seen or heard of anyone tripping over as a result of an undone shoe lace!
AIBU to think that this is "a swans wing can break your arm" and "going out with wet hair gives you flu" territory?!