the bridge is arranged a certain way (some of them have ridges in slightly different spots for the endpoint of each string) so restringing it would be... unpleasant. more involved than just the strings. some of them, the body of the guitar is shaped to hug your body. I can think of a few different guitars in the family collection and why it wouldn't work, but like, it's usually more complicated than just the strings

In a lot of cases the body of the guitar is different.

Some acoustic guitars like this one:

might work fine strung backwards; you might have to do a bit of alteration to the bridge and the nut, and you might put on a second pick guard, but you can probably Lefty that Righty.

A guitar with a bite taken out of the body like this:

That bite is so that it's easier to reach the base of the fretboard where the high pitch meedly meedly notes live. If you flip that guitar over, the notch is on the wrong side. You can still play it, but the point of that notch has been eliminated.

Acoustic-electric guitars, such as most Ovations, have their controls or built-in tuners on the sidewall that would face "up" when held and played, making that a pain to use upside down. Possibly literally if sitting down because the knobs would dig into your thigh.

Electric guitars like the Fender Stratocaster:

Are 1. surprisingly heavy because the body is solid wood, it's not hollow like an acoustic, and 2. are carved to fit a human body. You can see in that image the relief for your side in the back and for your elbow on the front. The tremolo lever ("whammy bar") is in an asymmetric location so that it can be both used and moved out of the way. The knobs and switch are convenient yet out of the way of strumming. The cord socket is designed to point the cord down and away. If you use this guitar upside down, you defeat all those ergonomics, the guitar would become difficult and uncomfortable to hold and use. Didn't stop Jimi Hendrix, who famously played a Stratocaster upside down.

I'm left handed and a guitarist, and I assert that a standard guitar IS left handed. The intricate work of fingering on the frets is done with the left hand, the large gross movements of strumming is done with the right. I'm perfectly comfortable using a standard guitar, yet most of the right handed people who have asked me to teach them to play have wanted to hold the guitar the other way, neck in right hand.

Jimi Hendrix famously did this, but it's not without its drawbacks. Some models are more problematic than others.

An acoustic like this would probably be pretty straightforward.