It sure looks like the main plot of this season is going to be Michael and the Disco crew figuring out what caused The Burn and fixing it, thereby restoring the Federation. Just for fun, let's translate that into a contemporary setting. Let's say a Turkish sailing ship from the 1400s is thrown forwards in time and washes up on the shore of the Mediterranean in 2020, and one of the first things they learn is that the Ottoman Empire fell 100 years ago after World War I.
"Ah," they say. "So all we have to do is find out what caused this 'World War I', undo it, and the Ottoman Empire will spring back into existence!"
Well, your scenario is off. For one thing, they don't know what caused the Burn. So, I can see this from both sides.
From the Federations point of view, it's something that happen over a century ago. They're don't like the new status quo but they're used to it. They grew up with it already being normal. So, the daily stuff is going to take precedent.
Michael on the other hand is shock by the change. It's not what she grew up with. To her, it basically just happened. Not the Burn, but the shock associated with it! She doesn't have that sense of it being normal and the acceptance of the status quo and the feeling it won't happen again are not ingrained.
I can understand both points of view.
And, yes, historians have looked at the cause of WW2 and have had ideas about preventing other wars. Look at the Marshall Plan after the War. (I just you said WW1, but historians study that too).
I don't buy that the Federation didn't fully investigate the Burn over the course of the century though. But, I suppose they were just so busy surviving. But we saw that two people in a freighter could get key information.
But I do understand the different reactions to it.