Thoughts on this rule?

The rules giveth and the rules taketh away. Golf is full of crap breaks and I believe anytime you can use the rules to your favor, do it!!! The more you know...

that's interesting, but what do you think of this?

You get relief, it is what it is, but there aren't paths and sprinkler heads everywhere, it's not like it happens every time your ball gets in trouble, it's kind of a rare thing so no big deal.

I mean. The rule is available to everyone so at the end of the day it’s fine. That said. I do think golf would be a much more interesting sport on the whole if there were no rules protecting/dictating the golfer’s stance. Whatever you gotta do to get club to ball where it lies

It would be interesting to see how it would play out with an actual @USGA rules official. The rule allows for the closest point of relief. Swinging left-handed, that would likely be on the other side of the cart path in your scenario (further away from the tree) further to the right of the right-handed golfer. Versus what you are hypothesizing as relief fully to the player’s left on the other side of the tree. Once full relief is established…likely on the other side of the path, then yes, the shot could be played right-handed. Here’s a good video explaining how the closest point applies.

Believe it or not, discussion on a golf rules site concluded that the left handed stance is subject to skill level, as in do you have the skill to actually advance the ball. So apparently this option is only available to "better" golfers.

How the hell do these idiots cover golf for a living and are just now finding out about this rule

You can only go the other side of the path if that’s the closest point of relief from the path. Given this circumstance you may have to drop closer to the tree or on a root, it is not relief for your best option. It’s relief from the path, then nearest point.

Has to be a reasonable swing. You can’t just say you’re going to play left handed so you can stand on sprinklers in the rough with no trees around

Yes the pros cheat a lot and use this rule to their advantage. About time you read the rule book.

Exact ruling happened to me except I play right but putt left But the drop,because I was on a cart path nearest relief was back towards where the ball was in first don’t get to drop it on the other side of the path Hit my putter made bogey