New York City/metro absolutely deals with “who’s the home team, and how does this affect the local TV schedule” every single week. If the Giants are at home on 1, the Jets are most likely to be a) going somewhere else and playing at a different time; b) on a bye week; or c) their opponent. The Jets are definitely not going to be at home at any point that Sunday, and probably won’t be the home team on any alternate date either unless they burn a home team designation playing in London or Timbuktu or wherever Rog wants an NFL game. This is the foremost drawback to sharing a stadium, and now the NFL’s two largest media markets’ teams all do it.
I hope it doesn’t impact the game either but the more devious thing to do is to play the west coast team traveling east in the early kick slots, especially now that bindings by division are less strenuous.