Of course there is a natural selection reason - symmetrical structures are stronger.
Of course there is a natural selection reason - symmetrical structures are stronger.
Symmetry is also challenging to maintain and very visible; any malformation is obvious. This is useful in showing health and genetic fitness to mates.
Many tasks are also inherently symmetrical, like locomotion. Evolving the two legs totally separately would be very error-prone and you'd never quite get it right. Having them both just be copies of the same structure is much cleaner and always efficiently completes the task.
Same for things like binocular vision, having ears that hear equally and so can easily echolocate, etc.
The decreased coding required is a nice bonus, which probably contributes.
Stronger under what condition? For the same amount of material? For the same amount of information needed to describe how to build the structure?
Do we see evidence of structures which don't require strength being more likely to evolve to be asymmetric?
Or do you just mean 'stronger' in a survival-of-the-fittest sense - symmetrical structures are fitter?
It's not at all obvious to me that this should be the case. Indeed, some very strong natural structures like shells are not symmetric at all.
Crabs are such a successful shape, crustaceans have evolved into it five separate times.