When it isn't your first team who lose it isn't usually a significant blow to morale. There are two small benefits to them losing that game from City's point of view: one is that it damages confidence, and the other is that it is a good team that City won't have to play. But they are well outweighed by their fewer fixtures.
So far we've been very lucky with cup draws that allow us to field a second string, but that won't last. What we don't want is to go into the last month or so of the season with a whole pile of big, demanding games (CL semis/final, FA Cup semis/final, rearranged league fixtures) whilst they have fewer, less demanding fixtures. If things are close that could give them the edge.
I know where you're coming from. If they'd lost that game in isolation I don't think it would have mattered much, it's after the City defeat it did - and rotating is all very well, but they ended up bringing on their key players anyway, having sat them in the cold for an hour. That's why the Brighton game is now a really big one for them, and one they have to win. If they do, yep, they can say they're back on track. If not, the pressure is seriously on.
As far as fixture congestion is concerned, yes, that's true, but it's the price of success, so it really is up to City there.