How would their playing a home game make them suffer exactly? The only have one home game in November, while switching the fixture to the Etihad would mean they have two.Again meaning City would suffer for your delay. We had to play 3 awaygames in a row last season in March and it's even worse a month later.
It's also worth pointing out that three of their four September fixtures and two of their three November ones are at home, so it's not like they'd suddenly be playing a string of away fixtures as a result. Quite the opposite, in fact. Equally worth pointing out is The FA didn't have a problem with switching our game with Watford at the start of September to be played at Watford's ground when it was originally scheduled to be at ours.
The only actual issue is that, as the match is scheduled for a Sunday, it's a mild inconvenience for whichever of Sky or BT is showing it. And that's what the real issue is, one The FA is proving themselves to be utterly spineless to address.
