Having the teachers learn is okay. Having them become so out of character and incompetent in order to make the Student Six look like better friends and teachers isn't. There are many reasons why Complete Crap Clause is such a disaster, which I don't need to explain in this paragraph. One episode later in S8, The End in Friend, shares a lot in common with it, but unlike its predecessor, it fixes NCC's primary issues.

Which ones? To go through them one by one:

1. One of the biggest differences is Dash's and Rarity's statuses. In NCC, both Dash and AJ were co-teaching their class about how to learn friendship through teamwork, but their egos got in the way of actually teaching the Student Six. Here, despite being teachers, they're not teaching the class. They're subjects for Twilight's class so she teaches them about how differences in passion don't fracture friendships.
    
2. Why did AJ and RD argue previously? Because they wanted to win Teacher of the Month, and their focus was on that over the students. That's not the case here. They actively try to work with each other to get past their differences as Twilight uses their experiences in real time to teach them. Or at least try to. Unfortunately, miscommunication or tastes get in the way of being able to see their interests in a positive light.
   
   When things boil over, it doesn't come at the cost of the Student Six looking better. Instead, they use their arguments as a teaching tool to learn what friendship means, even if it's not Twilight's intention. Notice how they quickly scribble notes before Act 1 closes followed by Smolder questioning their friendship as the moral is delivered. Additionally, their argument isn't petty and perfectly in character of each other. When they insulted each others' interests, they were rightfully angry. Their testiness was down to earth, and the episode treated it as a really big problem; Twilight and Starlight took their fighting seriously to the point of crafting an emergency plan to mend their friendship.
    
3. In addition to not coming at the Student Six's expense, it's even more evident by how other ponies react to their escalating argument.

   Quote

   Rarity: If you can't be bothered to read the thing I like, that just further illustrates the point that we have nothing in common anymore!

   Cherry Fizzy, Savoir Fare, Rose, Lyra Heartstrings, Sweetie Drops: [collective gasp]

   Rainbow Dash: At least we agree on that! From now on, I'm only hanging out with ponies who get me!

   Cherry Fizzy, Savoir Fare, Rose, Lyra Heartstrings, Sweetie Drops: [deeper collective gasp]

   The other ponies at the restaurant represent the Ponyville folk, and their reaction isn't comedic. They know quite well how close the Mane Eight are, including these two. When an argument as nasty as this endues, they notice, and it's very shocking. Ponyville can't afford to lose their tight bond. Lyra and Bon Bon showing grave concern in between gasps adds to the seriousness of their drama.

4. Rarity and Dash not only learn their lesson, but also take it to heart and stick to it.

5. Oh, yeah, TEiF doesn't have a teacher recklessly screw up at a certain yak's expense.

In addition to fixing Non-Complete Clause's problems, it borrows one key piece from Mare Do Well and its ripoff, 28 Pranks Later. But there are major differences here, too.

1. Even in Mare Do Well and 28 Pranks Later, they still didn't have to scheme Dash to teach her a lesson. In the latter, the RM5 become major hypocrites, because they get upset at her for putting more effort into the jokes after accusing her of being previously lazy. This mean-spirited tone is completely nonexistent in Twilight and Starlight's setup; the RM5's previous setups were reactive, while Starlight and Twilight's was proactive.
    
2. The purpose of their plan was to use their strengths, weaknesses, and interests so they can follow the trail (intentionally) left behind and rescue it. We know it was a setup, but Dash and Rarity were so absorbed in their argument that they didn't. Yet, when peril hit, they put the fate of Equestria above their feud (unlike NCC, which was the opposite).
   
   Adding the fact that this quest carried no sense of danger helps, too.
    
3. As they searched, their anger progressively eased. While in the swamp, they admired each others' tricks and ideas to solve the puzzles, including crossing the swamp, asking help to a Bufogren (who was also involved), and opening the passageway behind the School of Friendship. At points, they actually forgot about their fight, leading to the scene on the mountain. They realized how poorly they behaved and not only grew a sense of tolerance for their interests, but newfound respect, as well. This quest humbled them without humiliating them. And to borrow from @Cwanky's review, given the current climate regarding sports, politics, and cultures (including multiculturalism), the understanding and respect of diversity while sticking to our own values is integral to society today. The moral taught (and how) is incredibly important.

The teachers were as equal as the students: They, too, learned a valuable friendship lesson. But the episode carefully crafts it so it doesn't prop the students over them. And by sticking to the lesson and not devolve into an argument, The End in Friend concludes on a high note.

Oh, and all the horse jokes in this episode were quite funny.

In short, this was a really good episode.