The answer is simple, NPC 1 and 2 will never have that conversation, because they had that conversation many years ago before your character was ever born. Why do they need to repeat it again? That happened in the past, and they are living in the present.
So that's a yes then? You feel the game WILL take place more then a 1000 years later. Cause otherwise any Krogan or asari teammate is gonna remember just fine.
Whether you want it or not is irrelevant. Unless Bioware reboots the entire series from scratch, they have nowhere to go. Thinking they can somehow write an entire new trilogy that maintains pathways for all 3 endings is not realistic. Having ME4 take place in the past makes even less sense, humans haven't even been on the galactic stage that long. Placing it in parallel with the ME series would not be very sensible, either, how do you make it work with Shepard running around the galaxy? So the only real options are reboot or a few hundred years in the future.
Or they can pick one ending. Knights of the Old Republic did this, Prince of Persia did this, Legacy of Kain did this. I don't know why you don't see this as being an option.
The genophage could be cured by ME4, and how it got cured does not matter. The Krogan could have done it themselves for all we know, and they wont diverge how it got cured to you because you wont ask. You are a new character born in a different time, what do you care about Krogan history? The Asari might not talk about what happened hundreds of years ago, why would they? Its in the past, and your character in ME4 wont care about the past enough to ask. The relays will work, and again, your character wont care why they work, because they worked when you were born.
Cause they won't just be "augmented Asari" they'll be outright half-synthetic, half Asari. Pretending that the Synthetic endin just gave people a few perks is disregarding the entire reason the Child thought it needed to happen. It's suppose to give people a brandnew understanding of synthetic lifeforms that they otherwise would not have.
And how says a few hundred years will be enough in the Destroy ending. The Asari have been at the Citadel for 2700 years and they've never been able to understand the Mass Relay nor produce one of their own.
In other words, just because there are species that may have been alive and know what happened back then, that does not mean they will talk about it all the time. Its in the past.
Good lord, have you played an ME game? Every planet you visit comes with a summary of it's history. The Codex is full of history. even tho you rarely ask about it, the events of the First contact war, the genophage, the creation of the geth, the discovery of charon relay, the Protothean artifacts on Mars come up all the time.
Now we play a group of people who know don't anything, whose ships computers and databanks don't know anythig and are physically incapable of inquering about it. That's your solution?
If you think this sounds far fetched, just look around. The average American doesn't have a clue about the history of say, Japan, much less their own history. The average person in Japan or Europe probably can't name all the US presidents, or name a quarter of the 50 states. Many people don't care about things that happened before they were born, just like kids today have no idea what life was like before the internet, nor do they really care. The character you play as in ME4 wont care, they want to explore or accomplish whatever their mission is.
Most Americans know whether Hitler killed himself or survived to rebuild Jewish culture for a couple of decades/centuries. Though I'm not American so maybe not.
That would be your own problem then. Not the writers of the games. The Halo universe is bigger than Chief. The MEU is bigger than Shepard. Any universe is infinitely bigger than a single character. Your attachment to said character doesn't change that.
Mass Effect's universe is big, but not so big that the presence or absence of the Quarians, Krogsn, Rachni, Geth and Reapers would realisticaly go unnoticed. that's more then half the intelligent races that populate the ME galaxy.