Obviously you know this, but the brain does localize some functions to either hemisphere, just not in the way most people think it does. My vague memory from having taken a class in psycholinguistics is that people with aphasia who've had some part of their brain damaged are good evidence of this localization.
And it's also the case that even though certain brain functions are linked with specific locations, the brain can still use plasticity to re-organize things and adapt to damage. And when you're doing any language related task, there are always going to be other more domain-general brain functions involved too, which aren't as localized.
https://en.wikipedia.org/wiki/Wernicke%27s_area https://en.wikipedia.org/wiki/Broca%27s_area