Simple answer to the question?

No...

I think there are improvements, but as stated there lacks a cohesive arc structure. Cadmus is the arc that is not played to advantage. I really like the addition of Lena Luthor and Mon-El. While I am not necessarily into shiping, the on-scene banter between Melissa and Chris Wood is outstanding.

My favorite episodes of last year were "Falling " and the last two. I think "Exodus" is the best of the season this far and in some ways is comparable to my favorites of last season. I believe that if they focus on their story arc for this coming season, then we can have one that builds on the strengths of Season 1 and the targeted improvements of Season 2.

Argo

I appreciate the comments.
I do not get the same feeling of how heroic or strong she can be this season. Or how meaningful the dialogue was last season.
Taking on Red Tornado and blasting him into oblivion was awesome.
Taking on Non and pledging to defend Earth after being under the Black Mercy was inspiring.
Alex fighting to have Kara return from "Krypton" under the Black Mercy was outstanding.

I just have not seen/felt that from any of this season's episodes yet.
But I am still hoping for that level of emotion in an episode this season.

I reckon Season 2 has some improvements and some regressions. Rationally, and not speaking as the huge fan that I am, I believe in comparison to say The Flash right now, Supergirl produces stronger individual episodes but is weaker as a season. Main reason is still that for other DC shows I can always feel a Season Objective, so to speak, as to the main goal and obstacle of the season, while for Supergirl while I know it's supposed to be Cadmus, it still feels somewhat like a string of issues of the week, with the "main arc" showing up once in a while.

"Denouement" - a very appropriate word!
That's how I always end my fan fiction stories, with the equivalent of a "couch/ balcony" scene (but with more than just two characters). And of course, I've tried to do my own version of "world building", too

the writing is season 2 is so much better. Sure there were some standout episodes in season 1, but overall I would say the quality in season 2 is of a higher average.

The world building they have done in season 2 is amazing. They have fleshed out some of the ensemble cast giving them depth and stuff to do outside of Kara which is refreshing.

I know that many miss the couch/balcony scenes season 1 featured, but that was more a product of how an episode was structured. A problem was introduced and solved in the episode and the couch/balcony was the denouement of the episode's story. (the final word on this weeks lesson). The couch/balcony scenes still happen but not at the very end of the episode to wrap up the week, instead they might come in the middle of an episode sometimes even in the middle of the DEO, but it still serves as the denouement of a story line.

I know Mon-el is a divisive character, but his story is being told in such a brilliant manner. His entire story is being told through Kara's eyes, she is the narrator to his story. The only time he has a scene where he wasn't with Kara was 1. when he is doing something heroic (ie running into the bar to help during medusa, stopping to help the random homeless guy in changing) or 2 when he has his 'couch' scenes with Winn or Alex where his behavior alters after because he phases into the next chapter of his story. Otherwise all his scenes are with Kara because without his narrator his story doesn't get told.

Look at Lena, we have no idea if she is good or evil, and they play to it perfectly. In comparison would be Maxwell Lord who was basically a mustache twirling bad guy who was essentially afraid of the world around him. But you knew he was up to no good.