Hm. I still mostly disagree (on "Mane Six" fitting the group.) I hope I'm not sounding like Coily/Stantz here. So I'll have to address all of your points…bleh. Usually, I only have to address a couple. I probably won't link to much, because I woke up a little early, and I want to go back to sleep soon.
A reason I don't completely disagree is because I don't really know for sure how the dynamics will play out in Season 4. I'm confident that we're all speculating, but the show would have to make an unconfirmed change in focus for the Mane Six to be separate protagonists most of the time.
Another reason I don't completely disagree is because you're right in that Twilight was always separate from the rest of the Mane Six anyway. She's the student of Princess Celestia (we only know of one that Princess Celestia teaches and mentors.) She moved to Ponyville long after everyone else. Even as a bearer of an Element of Harmony, she wears a big crown thingy whereas everyone else wears necklaces. She's also a dirty tyrannical whore.
Fluttershy lives on the edge of Ponyville.
Applejack lives at the edge of Ponyville.
Rainbow Dash lives, um, above Ponyville?
Pinkie Pie lives in Ponyville.
Rarity lives in Ponyville.
Twilight Sparkle lived in Ponyville.
Remember that as I made that statement and posed the question, I was going partially on the knowledge that Twilight had her own castle/mansion outside of Ponyville. We don't really know where Twilight will live now. But for any princess, would you expect her to live in a library or would you expect her to live in a house befitting royalty?
There are many expectations of princesses in this universe from what we've seen so far (i.e., the similarities among Cadance, Luna, and Celestia.) If Twilight is a princess like them, then she would have the attributes which generally make the princesses appear above other characters. Characteristics that, yes, a role describes Twilight (if not defines Twilight) after the last episode.
So it appears that people are still downplaying the fact that Twilight is a princess in this universe.
However, it seems like a couple of people didn't see that as a point of separation anyway.
After all, here are six whose fates are inextricably intertwined, who share bonds unbreakable.
I think when we say (or at least when I think) "Mane Six," it's a pun of "Main" from "Main protagonists." It also implies (to me) that those protagonists are equally protagonists and in the same way.
I think that if you have episodes that focus on being a princess with royal duties that affect the well-being of a country and your lessons are about leadership where the other protagonists have lessons on friendship, then that feels more like the protagonists of the show aren't really together anymore. Thus the "Twilight Sparkle and five other ponies." That doesn't mean Pinkie Pie, Rarity, Applejack, Fluttershy, and Rainbow Dash aren't important in terms of being protagonists. I think it means they are separate protagonists from Twilight Sparkle.
Or more simply, I'll have to see if their fates are intertwined by more than being the Elements of Harmony. On the whole, the show has very little to do with the Elements of Harmony.
True, one of them now stands apart, but the truth is that she always did. It is simply more pronounced now.
I think that the further separation of Twilight isn't irrelevant in regards to them being a group of protagonists. Again, if Twilight is a princess like the other three we know of, then it makes sense in-universe for her to have an entirely different set of day-to-day events that far exceed the differences among taking care of animals or running a boutique.
As long as the six are still friends, and still interact, I’ll always see them as the mane six.
Again, my understanding of Mane Six is that they are equally and similarly the main protagonists. Friendship is irrelevant to how I define Mane Six if I had to sit down and think about it (as I am now), and I'm not sure if it makes sense for them to have the same level of interaction anymore. At any point, Rarity could pop up in an episode to help out Pinkie Pie with a problem.
If Twilight "happens to be on a walk" in Ponyville (again, assuming she has a significant role and duties as a princess) to help Applejack find Apple Bloom or something, and she ends up in more than, say, 2-3 episodes of an inconsequential matter, I'll have my suspension of belief threatened. The coronation didn't do that too much, actually. But her frequent appearance at casual events while serving the role as princess would.
Now to appeal to ZeroBlue, if Rainbow Dash was a princess, then I'd say it makes perfect sense for her to bail out on her duties if she wanted to fly around or take some time off. She'd fulfill her duties, and her leadership style would certainly be different. But Dash will fly and Dash will hang out with her friends.
Twilight is a workaholic. Even her time with friends is scheduled in literally minute detail. Something's got to give in terms of core, probably-shouldn't-change-all-that-much personality (e.g.., attention to detail, curiosity, awkwardness) or world building in order for her to be with her friends like always. (I do expect to see some aspects of Twilight change. I'm generally OK with her not being quite as panicky as she was before.) I'd rather see Equestria make sense and Twilight's core personality be maintained than see Twilight stay together with her friends in the same way.
The way Celestia tells Twilight she won’t be her student in the same way as before makes me think that friendship lessons are just going to get replaced by HARDCORE PRINCESS MAGIC AND/OR LEADERSHIP CLASSES, but the dynamic will stay the same.
I'm not sure if you can sell me that the dynamic between Twilight and her friends will stay the same. I think that's why some people think that a coronation would have been a good point to end the series. Not only is it an ultimate goal (or at least a huge turning point) for Twilight. The fact that lessons of friendship and lessons of leadership is a noted potential difference indicates that they'd have diffferent day-to-day lives that aren't likely to lead into learning the same lesson.
…Umm… Hate to break it to you, but I feel that is something that has always be a thing. There has never been a time this was not a thing…There’s so far, still six, and they are still part of the same team with the main focus.
There's a consensus that it is a thing though. And again, Mane Six seems to denote that the main six characters are similar in their roles as protagonists and are tied in their roles as protagonists.
If the show takes on an arc-based set-up, then I could see the Mane Six being intact. They'd all be bound by having similar adventures.
What I say is in relation to what made them similar main protagonists prior to the coronation: misadventures (e.g., babysitting, making dresses for a formal event) that can sometimes threaten Equestria in a more humorous way e.g., Spike is rampaging after turning into a massive monster, Cerberus escaped from the gates of Hell) that's resolved at the end of the episode than a serious way (i.e., King Sombrero, Swiss cheese, Dark and Broody with Envy, Chaos Incarnate)
Again, the show stands just as well without epic adventures or a bound destiny. I think "Mane Six" just focuses on what makes them protagonists of the show ("Mane" characters or protagonists numbering six). I think that's mostly their less threatening day-to-day events.