Specifically referring to those four stories...
A) Azir's stories are fine, but they raise questions, not answers. How did Azir get resurrected by Sivir's blood? She's related to him and magic is involved somehow, but how can Sivir be related to Azir when Azir's entire family died? There are any number of explanations, but we have absolutely nothing to go on, so there's no point in speculating. I remember a Rioter getting annoyed that we were asking for answers about that, instead of just speculating to ourselves, but we don't have any hints as to what happened, so what are we supposed to speculate on? There's also the fact that almost all of Riot's recent lore releases have been about new things, with the exception of Amumu's little video. They raise questions about a champion, but since we have no guarantee Riot'll ever get around to answering them, we don't really care.
B) Kalista is a spirit of vengeance. Offer yourself to her and she will get back at someone who wronged you.
...That is all we have to go on. A video, a short bio, and a long story, and they all say the same thing. Again, this is a problem of raising questions that are not getting answered. It's like instead of including a short bio for people who don't care and a longer story for people who do care, Riot just decided to make the short bio and the long bio the same thing, just one has more words in it. Invocation is more about the sword-wife that Kalista pacts with than Kalista herself.
C) This is good, primarily because this is a champion that Riot's primary long story concept works on. This also happened to Kalista and Amumu's longer lore, and to a lesser extent Gnar's, but Riot's been fond of having some normal denizen of Runeterra (or Rengar, in Gnar's case) react to the champion, to make them look larger than life, and make them truly worthy of being called a 'champion'. The problem is that these stories are actually about the point of view character; we empathize more with the narrator than the champion. This works for Rek'Sai because she's less of a character and more of a hazard, but none of the other three have anything explained about them. This shows us that their origins are shrouded in mystery to the average denizen of Runeterra, but we're not the average denizen of Runeterra, especially now that summoners are not a thing. We should not be guessing about every single champion that has been released since the retcon; it gets boring. It's like a series of murder mysteries that never explains the murderer; it just skips from one to another and you're still wondering 'Did the Butler from the first case do it?'
D) Bard's entire thing is being cryptic, which wouldn't be a problem if, again, I didn't think that narrative will never get back to him and therefore speculation is pointless. I learned more from having Rioters explain the video than actually watching the video. It's nice, but it's not something I can get my teeth into and analyze, you know?
And as for Echo...that short form lore is the worst I've seen since Rammus'. It's just badly written (it sounds like a elementary schooler doing a book report; it's just a listing of his most sapient features, with no rhyme or reason to placement.) I'm going to rewrite it right now:
A prodigy from the rough streets of Zaun, Ekko uses his invention, the Zero-Drive, to explore the branching possibilities of reality and twist any situation to his advantage. Whenever he's not experimenting with multi-dimensional probability, he can be found running wild with the other lost children of Zaun. He revels in this freedom, and whenever something tries to threaten his friends, he's willing to endure anything to defend them.'
Same basic words, just put together in a way that the sentences actually flow. (I removed the last sentence because it just felt like a tagline to an action figure, which is kinda what lore is reading as to me recently.)
The video, meanwhile, falls under the same thing that the Azir video does; it raises more questions than it answers. The only things it states are Ekko's abilities and his basic philosophy. It doesn't explain who the memorial is for, who he's fighting against, why he's fighting against him, etc. It just raises a bunch of questions that narrative will fail to answer.
Honestly, I don't have many problems with the launch stories themselves. But I want things other than launch stories; I want actual character development, not just character establishment. All Narrative seems to exist for is to write little story blurbs and cool advertisements for new stuff.