Indeed, the ICC has acknowledged the difficult situation. It is also difficult task for them to solve it. On the one hand Pakistan will host and on the other hand India will not play. It seems that cricket is private property. He will do whatever he wants. If we look at FIFA, the decision they will give will be final there is no room for dissent. Even in this case, if the ICC had played that role, then there would not have been any adverse reaction between these two countries.
You can never compare the ICC with FIFA. ICC has just 12 full members. On the other hand, FIFA has more than 200 members, and all of them have equal voting rights. So it is possible in the ICC to have one or two members dominating the entire policy making process. But in FIFA, it is more difficult (but not impossible, as we saw how Qatar won the hosting rights for the world cup). Personally, I believe that Jay Shah's statement was in bad taste and amounts to abuse of power. There is no reason to demand Asia Cup to be shifted out of Pakistan.
Yes, I definitely can't compare ICC with FIFA. I know FIFA's position belongs to very high and have more members. Also there are more than billions of dollars involved in everyday. One of the most prosperous organization in the world. Can't be compared to them but there's nothing wrong with following them. Maybe there will be some obstacles too. But there are some things like biased behavior, focusing only on pecuniary interest etc. Which should be avoid by ICC. There will be no harm in following the positivities or the good aspects.