You could even do that on the player's model specifically. But it's still a maybe, you're almost guaranteed to get some cursed bugs due to every preexisting code having been made with right handedness in mind.

I'm sure animators are internally screaming at the reasons why this will make some originally right handed animations look off but that's not my area of expertise.

In reality it's probably not the hardest thing to do gameplay-wise, especially if you're doing it from the very beginning of the project, but I don't think you can simply mirror animations (and some animations-related logic) and have it look natural, so you'd have to make dedicated animations and possibly logic for left hand strikes, right hand blocks etc. which would obviously be much more expensive. But yeah that's probably what Minecraft does now for example, and since they have a very low level of detail on player characters and their animations it looks alright.