Don't know, does walking with one leg make you a better runner? I doubt it, there would be more efficient exercises you could do since their union is more valuable than dissonance.
Though there is some weird dominant brain stuff you could meddle with, look up split brain patient studies for some idea on what it could lead to.
I would imagine doing muscle training on one leg a time would help significantly, both physically and mentally. But mainly physically as far as the leg goes. If you could isolate 'simulating' running with just one leg I would completely imagine it would help with running with both.
But running, as with seeing etc, is a two item thing. So obviously the actual final act needs "trained" with both.
I don't think training separately to improve a task that uses both is worthwhile, you might as well just do more intense training with both. For martial arts or climbing however it would be worth training them separately, but that is a task where they are used separately for separate tasks. Individual eye training would be good for telescopes, being a pirate and scopes or firearms.
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