Is Rey (who fended for herself with melee weapons her whole life) beating an untrained, shot-in-the-kidney-and-bleeding-out Kylo somehow more egregious than Luke (who (IIRC) never got any lightsaber training) beating the defined best Jedi/Sith fighter in the galaxy because he let his anger control him? The fact that luke got his ass handed to him twice doesn't make him winning the third time somehow make any more sense within the framework. It works because of the expectation of the metanarrative structure, or because of non-diagetic assumptions (Vader didn't want to kill his kid, was getting old, etc.), not because of anything explicit in the movie.

With respects to both sides, the directors of both A New Hope and The Last Jedi have shown bits and pieces of light saber training.

In a New Hope, there are moments on the Millennium Falcon where Ben is teaching Luke (if you'll remember with the helmet and little floaty droid) how to block lasers by using the force. While it's not very conclusive and isn't very long, people seem to forget that this is the director showing you that Luke is being trained to use a light saber, regardless of whatever else you'd like to think.

Extremely similarly, on the island with Luke- there is a pretty explicit scene where Rey is swinging her spear around and eventually the light saber. While it's not the longest or most comprehensive scene, it still shows that she's trying to teach herself how to fight. I really don't understand when people are confused as to how Rey knows how to fight, the writers and director literally put a scene in there to show us she's trying to learn this.

Now, say what you will about the length of training or comprehensiveness of it, they still exist. If you believe Rey's training with a light saber scene was too short- that's a valid criticism. I personally liked it because too much training would have been boring to me, and it worked very well in A New Hope so I didn't mind.

TL:DR-I enjoyed and agreed with your analysis. I just gave a little more evidence on this claim.