Abstergo and Animus - yes. The rest (introducing to Assassins, Templars and artifacts) is successfully done by past settings and remark by Lucy "oh, Assassins and Templars exist today as well, look I am an Assassin as well". And regarding to "finding out more who Desmond is" - if I don't understand what's his background, why should I care about him? It was criticised during the days Desmond lived as well.
As for interesting conversations - I can't consider conversations with Vidic interesting, when you ask what does he want and as answer you just get replies similar "show to us where this is!". What "this"? Is that a meaningful conversation? I'd rather go back to the Animus and explore historical setting. I understand the concept of what was intended, but there were flaws.
Altaïr's story doesn't tell you anything about Assassins and Templars existing during the modern era - it only shows you that they existed when they historically did. Desmond's story in AC1 develops the state of both organisations as of 2012. If you only remember the Assassins being mentioned by Lucy by her revealing she is one as well (not particularly fond of dumbing down that reveal like you just did to prove a point that it was poorly done - I don't think anyone thought that was poorly done), I suggest playing the game again or refreshing your memory reading the conversations on the wiki: https://assassinscreed.fandom.com/wiki/21st_century_conversations
Through the conversations Desmond has with Lucy and Vidic you learn where Desmond grew up, why he fled the Farm, how Abstergo was able to find him, why they went after him - his background really isn't vague at all. The conversations we have with Vidic are when the player finds out about Those Who Came Before, you learn more about how the Animus works and why it was created and how Abstergo works. There is not a single point where Vidic refuses to have a conversation with you and instead says "show us where this is!" - he will always have something to say, whether he berates you or not.
AC1's conversations and emails weren't criticised for not being well-written or not revealing enough. The modern day was criticised because people thought it pulled them away from the historical parts and because Desmond wasn't cool like Altaïr - the same reason every instance of MD gets criticised.
As well as Odyssey does. The difference is how it was shown - through emails. I might agree that the way it establishes relationships between newcomer Layla and old Assassin members are not the best, but nonetheless it is developing.
Which is my point. Layla never actually talks about herself with anyone, or shows interest in finding out about others. The only way you can find out about her is through files on her laptop. That is not engaging content, and is quite frankly a huge step backwards from how Desmond's character and backstory was developed.
Because Brotherhood, as much as I like this game, for me looks like a cut-out part from AC2. Comparison with Bayek is strange, bc he didn't receive a sequel and I suspect he never will. As for Brotherhood, Revelations and AC3 - I actually don't have anything against about MD progression there, as I said before, because they actually start progressing the story
Brotherhood continuing Ezio's memories should have no bearing on whether Desmond's story in AC2 is good or not. By the same logic, Brotherhood isn't good because Desmond continues exploring Ezio's memories in Revelations. Just because all of Ezio's story wasn't contained in one game doesn't make AC2's MD content bad.
Hold on a second, what about her conversations with Berg and Sofia? When the higher-up Templars consider her as nobody, and Sofia particularly steals her ideas and use as her own? That establishes a foundation for her to rethink her life, her choices, and accept William Miles offer. Again, I might agree that the way it is shown is not as good as we wanted, but nonetheless it is present.
Layla's conversation with Berg in Origins is a squabble about a parking spot. In Odyssey's latest Heir of Memories quest it's just Berg threatening Layla, there is no back-and-forth. I do agree the conversations with Sofia are good development, but that harkens back to the earlier point - considering that it's just in emails, we don't see Layla develop as a character because of the events described. We don't see or hear her emotions. We don't see her grow because of it. Sofia's treatment of Layla is what drives Layla to want to prove herself in Origins, but that's the kind of important setup to a character you need to show. Relegating so much character and story development to files on a computer that you can skip entirely does not make Origins' and Odyssey's MD better than Desmond's story.
Now for Odyssey. I don't argue at all on the fact that MD has its huge flaws (specifically I criticised that Altair II ship wasn't shown, it could've been a great addition), but if you take the development as it is without the ways how it was delivered - then it advances the story at least as well as Desmond arc story.
I do agree seeing the Altaïr II would have been very cool, considering we didn't see it in AC3 either, but I can't complain too much about it. But it is just impossible to not critique any content for the way it is delivered. Optionally reading up on things is never as good as seeing them or even being told about them. Even if Layla's story in the MD files was shown or told rather than relegated to emails, then the stories in Origins and Odyssey still lack the same character development we had in Desmond's story, or all the interesting conversations to learn more about other characters and the state of the world.
I won't deny that Layla already did more in two games than Desmond did in two games. But it's not about getting to the finish line as fast as possible. It's about developing the journey.
EDIT:
Which is revealed only at the end of the game out of nowhere. Just stating the obvious.
It doesn't come out of nowhere. The whole game Lucy talks about the importance of the vault and of what big interest it was to Clay, then there is all the build-up in Ezio's story about what's hidden in the vault, and Those Who Came Before were already teased in AC1. The retransmissions in Origins come just as out of nowhere.