Carbon nanotubes are cool, but i will believe space elevators possible once someone shows me a carbon nanotube rope i can climb with. I'd settle for a bike or motorcycle chain. A nanotube-based shoelace would be worth a noble prize or two.
On a practical note, if you drop something on your foot you need to be able to take your shoe off quickly - cutting the laces is often the best approach. Shoe laces as strong as steel would likely lead to you losing your foot. Same goes for titanium wedding rings...
Fyi, the military has a specific way to lace boots so the laces can most easily be cut to remove the boot.