Let me fix this for you: "Tell that to the people trying to take a nap with a screaming child or loud adults in the room below them, the people who need an inhaler just being around people who smoke/reek of perfume or don't practice good hygiene or the child that gets out in a busy place and ends up dead."
Yes, but hotels are for people.
I think what has me the most amazed about "people like you", is that you haven't even been to Disney while this new benefit is being tested. You have not seen what accommodations they will provide for you. There are at least 15 other Disney hotels, in all price points, that you can stay at that will be dog free (other than service animals, which are a lot more prevalent than you realize). How do you know a service dog hasn't already stayed in the room you are about to check into? Service animals are not magically hair/dander free.
I am not dismissing your health concerns but I also think you are not being realistic about the potential impact and how limited it is likely to be.