This is why I like switching stances. It is almost impossible to cut angles like that without switching to reposition yourself.
EDIT: didn't realize there was a discussion on stance switching happening, just finished reading the other posts. I personally think that if you want to be a stance switcher its best to either learn both equally or only ever use them in combinations and quickly switch back to your original stance. Don't be one of those guys who learns a stance well and half-asses the other one. This is because every time you switch to your half asses stance you are pretty much making yourself weaker while not facilitating the advantages of the opposite stance (because you suck at it).
I myself started training in a traditional art so I was thought to have both equally. First few months I was biased towards orthodox but after one particular sparring session I dedicated myself to learning both stances equally. I went into wrestling as well after a while of training and in grappling being able to switch is really useful and most people do it without making a fuss (kicking arts also more often seem to be tolerant towards stance switching than boxing). I do both stances equally. It honestly isn't as hard as some people make it out to be and it makes you A LOT more ambidextrous and you end up having power and speed in both hands. Though I am left footed and right handed so that might have made it a little easier. And obviously I am not a pro and have never even competed (yet).
One thing that I found difficult was not constantly having my weight on my dominant foot. My weight was always on my front foot in orthodox and back foot in southpaw. That was one of the issues that took a lot longer to fix. Though something I have thought about often is what if I never switched stances and started my training from the very beginning constantly as a southpaw or orthodox. How much better would my single stance be than my current double stances.
I honestly reckon it wouldn't be much better because at first it is hard to learn the opposite same move in the other stance. But once you do everything in both stances for a while you quickly start picking up new things much more easily in the opposite stance. At some point when you do something in one stance you can almost immidiately repeat it in the opposite stance. I regularly do a combo in one stance and then do it again in the other when I shadowbox. Your brain is flexible and becomes used to it quickly (this is why I think the earlier you start stance switching in your training the more you will probably pick it up).
Once you have started making both stances at about a similar level you can start experimenting with the more advanced stuff like combo switching, cutting angles with switches, facilitating advantages from both stances (e.g. trap more in sp, jab/hook more in orthodox, more 1/2s in orthodox, and so on). Although cutting angles with switches can sometimes come without much focus on it as you may randomly switch stances in sparring to get a dominant angle. I think that using switching to cut angles is probably the best advanced use of stance switching you can make. It works very well and there isn't very much risk involved like switching while leaping in or switching mid-combination. There are other little advantages to switching as well like protecting a damaged leg, being unpredictable and coming in random stances against some one who has to gameplan for you, not many other people do it therefore it is hard to train for, etc.
I would also recommend (after a while of training switching) to go into sparring classes and attempt to stay in a single stance for prolonged periods. This allows you to have control over your stance switching and do it more voluntarily rather than involuntarily without realizing that you have even done it. This also teaches you to be able to stay in one stance just in case you need to stay in that stance against some one as part of a game plan (e.g. I would probably spend most of my time in southpaw if I fought Johnny Hendrix).
And it is strange that we almost never see stance switching in boxing (though it may happen more often than I think as I don't watch enough boxing). It might just be that they know better than us or because of biases that have existed in the art and have been passed on for generations. Not bashing boxing (not even saying that this is what happened) as most martial art instructors do this. Though I noticed that Mike Tyson switches stances while throwing combos. Also Willie Pep would leap inside with switches a lot. And to the guy who blames Benavidez loss against DJ to stance switching, remember that DJ does it A LOT more than Benavidez and seems to be equal in both stances to me. While Benavidez is mostly a sp and I would imagine he is a little uncomfortable in orthodox.