Re: ATLA / Legend of Korra - PSA: Korra and Asami are canon!
I'd write a lengthy response but I'm genuinely baffled by what you wanted from Korra and Asami to make their relationship "genuine" like the others.
Let's say things went exactly the same but we change the characters a bit. Let's make some other guy be in Mako's position in Book 1 and 2 so all of the development they had there is non-existent beyond friendship, and then Book 3 and 4 has Mako and Korra getting closer.
3x01: Mako cheers Korra up after press conference. The two exchange a look with Korra's awkward ex. They have their driving lesson and make fun of him, as well as talk about how nice it is that they’re friends.
3x02: Mako decides to take a vacation from work and fly a luxury airship around the Earth Kingdom for Korra. When he first shows up with the airship there’s some major posing. Korra later toys with ex in an airbending twister for Mako’s amusement
3x03: Mako and Korra go to collect taxes for the Earth Queen together and end up kicking everyone’s ass
3x04: Mako and Korra spar to let Korra take out her frustration
3x05: They’re like, around each other but they’re just getting introduced to Zaofu. Not really a moment
3x06: They’re sitting next to each other at breakfast when Varrick uses his magnets?
3x08: Again, sitting next to each other at breakfast when Varrick shows them his airbender tester. The rest is Team Avatar trying to figure out if Aiwei is guilty and then taking off at the end of the episode.
3x09: The Stakeout. When Asami/Bolin go into town, Mako asks Korra if she’s okay, the two search for clues about Aiwei. Later Mako escapes from Ming-Hua and Ghazan with Korra’s body on the back of Naga. They get captured and Korra asks if he’s okay.
3x10: Long Live the Earth Queen. It’s the airship episode. They flirt/eye-diddly the entire episode and at the end Korra brags about Mako to Tonraq.
3x11: Mako offers to watch over Korra’s body as she meditates
3x12: Korra says she’s going to turn herself in to Zaheer, Mako says there’s that Korra “can’t expect us to sit by and let Zaheer take you.” They hug and tell each other to be careful.
3x13: Korra almost dies, Mako looks shattered. Then we get the scene at the end with Mako saying he’s there for Korra, taking care of her, checking on how Korra’s reacting to everyone, and standing with Korra and her family on the opposite side of the stage as Korra’s friends for Jinora’s ceremony.
4x01: Mako is grossed out by Wu's flirting with Asami, and we learn that Mako spent the past 3 years rebuilding the infrastructure to marry spirits and the physical world (plus Korra’s statue) with Asami. Mako also expresses excitement abut seeing Korra again, makes Korra blush over admiring her new looks.
4x02: We learn that Mako offered to go with Korra to the SWT. Mako also writes to Korra and is the only one to ask how Korra’s doing. Korra later reciprocates by only writing to Mako and conveying her concerns, asking Mako to not tell Bolin and Asami, because she doesn’t think they’d understand.
4x05: Mako’s upset about life so he goes to work out his problems in Avatar Park near the statue of Korra.
4x07: The Reunion. We get overt flirting, a lover’s spat, and then the two of them fighting in perfect synchronization while a bemused Asami is dragged along for the ride.
4x08: Mako brings Korra tea and comforts her
4x10: Korra defends Mako’s decision not to help build a bomb.
4x11: Team Avatar goes to hunt down Kuvira. Not really anything explicitly Makorra, but they’re around each other.
4x12: It’s part 1 of the finale, where Mako is working to help get Asami's hummingbird suits up. Korra places all stock in Mako's ability to help Asami, saying it’s their only chance, fights in synchronization with Mako again to bring Mega Maid to the water and freeze it in place for Mako, looks horrified for Mako’s sake when Bolin is killed, then looks angry as diddly at Kuvira at the very end
4x13: Final episode. Mako is the one to notice Korra come back from the Spirit World, the first to touch her after Kuvira’s arrest, and it looks like Mako places his head on Korra’s shoulder for the group hug in a zoomed in screencap. Then they essentially elope together on their vacation.
(Edited from this:
LoK Gifs & Musings)
They'd become friends, bonding over the strengths they have as people. They'd become closer than ever both emotionally and physically. When the season ends with Mako seeing Korra broken physically and emotionally, he looks devastated. He is the only one to get replies from Korra. Essentially thinks Korra looks good, Korra is embarrassed but pleased by it, they continue to bond and grow closer, then it ends with them going on "vacation" as they hold hands and stare intimately at each other in a light that represents the marriage of two worlds and a new era of hope.