I see the point, and understood it when I wrote my comment. However, as far as I know (and I could be wrong), there is no characteristic of either cerebral hemisphere determined at the embryonic stage that differentiates one from the other. As such the two hemispheres become functionally distinct but are not functionally distinct in principle or by virtue of being left or right.

Also, as others point out, hemispherotomies and -ectomies and to a lesser extent corpus callosotomies show that neither hemisphere nor their intercommunicative ability are strictly necessary for brain function. Yes, for ideal function, but that can be said of kidneys too.

Do add to this if you can argue against it.