They would care though if they lost money and moving the World Cup to November/December might just result in that. The North American market is already difficult enough, they are just about to have a foot in the door there. The next World Cup is in Russia, which already has a significant time difference in a bad way. The time difference to Qatar is either the same or an hour more, one way or the other, it doesn't help and putting the World Cup during football season helps even less.
I also doubt that it's a good time regarding Christmas shopping/holiday sells. There would be little time for stores to have memorabilia connected to the new World Champion ready for Christmas and I'm sure there are several people who will have done their Christmas shopping by the time they do.
I'm also wondering about travel - I think there were several people who combined a vacation with the world cup last year, I'm not so sure many would do the same with Qatar to begin with and at that date probably even less. Children don't have vacations anywhere in Europe at the time so dad's won't be able to take their sons on a world cup trip. I'm sure there are other aspects as well.