It just seems weird to me that you'd call that "the characters finally getting a life of their own" when to me s3 is bascically exactly the opposite. To me s2 fulfills "life of their own" way more because the storylines were actually progressing without Kara. It just seems like a huge contrast when what sparked the discussion originally was praise for Legends for Tomorrow because Legends actually lets non-main characters have storylines together and then people turn around and say James (despite not doing much) feels like he "matters" again just because he is doing nothing next to Kara than last season when he got a storyline about slowly bonding with Winn which imo culimnated/climaxed when James told Winn he considers him a brother now. On Legends, nobody would ever consider that character and relationship development somehow does not count just because Sara is not around when Mick has a deep storyline about his messed up father supported by Nate or just because Sara so far has paid little attention to the Amaya/Zari/Totem storyline.
For the record, I don't think that s2 had flawless or great writing either, but imo the "nuts and bolt" writing is just so much worse in s3 and particularly for supporting characters, it's been a huge drowngrade, particularly due to
1.) this tendency for storylines to just stop/the associated characters to disappear without in show explanation or reason and then resume again at a later point even though that's not how normal people would react to situations. Ie if your dad who you thought was dead and who was abused and tortured for years was back in your life that would be a big deal to you. The show could have solved this by throwaway lines (if I didn't want to show it on screen) like "I'm taking some time off to spend with my father" or "my father right now is doing X, he is fine, thanks for asking".
2.) character relationships take completely unrealistic leaps without the show providing the scenes to justify them. The show constantly uses scenes that never actually happened/they never bothered to show us tp justify moves it makes. The James/Lena move in episode 9 could easily have been improved by like one scene where Kara calls him out on liking Lena in a previous episode and them talking about it and maybe the occasional throwaway line by Kara about how Lena is (like when he came to the DEO to sing the praises of Karamel). That would have shown his point of view, better built up James and Lena by letting us actually know more about what he feels for her (is it a crush? sexual attraction? feeling protective of her? is he weirded out by being romantically fond a Luthor? hesistant to pursue it because she is his boss? insecure about her wanting him or him fitting into her life?) and built up the James/Kara friendship a bit more and let it feel more natural. Or do the opposite, have Lena confide in Kara about digging James before 9 or have Kara or Sam call her out on it or at least exchange knowing looks any time before 2 seconds beforer Lena and James jump each other. The show didn't even bother to tell us what happened after the kiss? We see them walking the streets together, so what happened? Did they sleep together? Did they feel the kiss was a mistake and agreed to go back being professionals? Did they agree to try and date? I feel like I have no idea what the current state of James and Lena's relationship is because the show didn't bother to show us their feelings after the kiss just like they didn't bother showing us the scenes of what Kara referenced had been going on between them. Things just "happen" rather than events and scenes leading into each other.
I don't fault anybody for LIKING s3 better, but to me statements like "characters getting a life of their own" (indicating that that wasn't the case before) or that this season has been good for supporting characters are just not justified by what I see on screen. There has been a lot of clumsy writing this season and supporting characters are particularly hit hard by it.
==> That doesn't mean that s3 can't be better by most people's metrics. Kara and Alex ARE the main characters so if those two have more consistent writing now that is worth it a lot to make the show feel more consistent overall. But imo on the fringes, the writing has been cutting a lot of corners and imo the supporting storylines and relationships are hit particularly hard by it. And to me that comes across as the show not really respecting those supporting characters if they don't bother writing them consistently and have them react to the events in their lives in any kind of realistic fashion.
I do think the show dropped the ball on James Guardian storyline in s2 for example by tying it back in thematically with Mon-El's heroism story. But to me it still felt like a logical progression. James wants to be a hero, James intiates steps to make it happen, James encounters obstacles (like when Guardian is framed for murder), which is what one would expect to happen and overcomes them, James is found out by Kara and it leads to conflict, James deals with "leadership problems" when Winn's girlfriend wants on the team, James encounters limits to what he can achieve as Guardian when he realizes that people don't look up to him the way they look up to Supergirl. They picked a topic for him and explored various angles of it.
James and Lena dealing with running CatCo together is a concept that looks neat on paper but so far nothing has been done with it. In ep2 James was upset that Lena didn't invite him for meetings, Lena indicated that she would bring him along to meetings now. This is the extent of "stories about running CatCo". Oh right, there was this throwaway conversation where Lena wants to run ads that are disguised as articles (one of things that are commonly considered one of the shittiest popular journalism practises), James doesn't like it, but with one throwaway line it is decided that it should be done anyway. Them clashing over this could easily have been an entire episode B plot. None of this has lead to meaningful actual storylines to explore this concept, something that was the case with Guardian (James deals with being framed, James deals with Winn getting injured on the job, James clashes with Kara over whether as a human he is strong enough to put himself into danger, James deals with leadership decisions, James deals with whether he is not inspiring enough).
BTW, speaking of things that were not followed up on, remember how the reason started with it looking like Kara and Reign were sharing a dream? Which was all weird because it looked like Alura was in Sam's dream too? The creature from Reign's dream showed up again when she had a vision of the hologramm lady and there was something that could be a veiled reference when Kara and Sam both mentioned that they've been having trouble sleeping. But other than that? There's been no progress on that whatsoever, I'm not even sure whether they just forgot about that.