I’m left-handed, and play left-handed guitar. This is an issue I’m very familiar with.
When I first started to play, I tried holding a guitar in the right-handed position, and then in the left-handed position. For me, the latter felt natural and the former felt quite awkward, so I chose to go left-handed. This natural hand position – dominant hand close to the body, non-dominant hand held out – is seen in other things, such as boxing and shooting a long gun. For some people, this is not much of an issue; others, like me, are very sensitive to it.
When I was looking to buy a guitar, I was in a shop that had no left-handed models. The salesman said I would have an advantage playing right-handed, as I could use my dominant hand for the fretting, which is the biggest hurdle for a beginning player. My thought was, if it’s such a wonderful advantage, why don’t music stores stock mostly left-handed guitars for the benefit of all the right-handed people out there (~90% of the population)? The answer, of course, is that there’s more than just fretting involved.
All things considered, I would say that if you’re right-handed, by all means go for a righty guitar unless you feel a COMPELLING reason to play left-handed. Playing left-handed will pose a limit on your strumming/picking that will likely become significant once you reach a certain level of ability. It also poses a serious limit on your selection of guitars to buy, the ease of reselling them, and the ability to play someone else’s. I’m thinking you’d just about have to cringe at the prospect of playing right-handed to make going for a lefty guitar a good idea.
For lefties, it’s more of a muddle. Some (like Paul McCartney and me) feel compelled to go with the “normal” position for our left-side dominance. Others (like Jimi Hendrix and Elizabeth Cotton) use a righty guitar but play it in a lefty position, upside down – solves the availability problem, but requires unorthodox fretting. And probably about half (like the above-named Michael Hedges) choose to just play right-handed. It depends on which of the various challenges an individual finds most easy to deal with.
But back to the premise in the OP: be assured, for the various reasons mentioned in this thread, that if playing a lefty guitar was truly advantageous for right-handed people, then most righties would be doing just that.