WDW could build a resort that caters to pets, and it is probable many non-pet owners and owners not traveling with their pets would be willing to stay there. However, there would be no guarantee of enough demand throughout the year to warrant the expense of a whole resort complex.
If they built a wing on an existing resort, the biggest concern would be the ability to shift guest to those rooms. For instance, if all "non-pet" rooms are currently filled, the resort management would simply channel the next guest to the pet room (just like they do with HA rooms and previously smoking rooms). However, it would take only one guest that is deathly allergic to pets to be moved to the pet wing to cause a significant issue (WDW is now toally non-smoking for a reason, right?).
Although this is very unlikely, it is more probable WDW reservations would need to play "musical guest" as many visitors would not want to stay in a room regularly catering to pets.
Jade, I am very surprised by this recurring comment, as you are well traveled at WDW and know that requesting a non-pet room would be just that; a request. WDW could put people into a pet room, regardless of needs or desires.
Here is the bottom line on these arguments, pets are property, plain and simple. They have the same fundamental rights as luggage, an iPad, cigarettes and a handgun when it comes to the ability of a private property owner to ban them from their land (this is simplified, as pets do have a few rights to humane treatment and upkeep, but vacationing isn't one of them

).
Children, on the other hand, are human beings with a substantial amount of rights, thus is it not accurate to compare a dog to an infant (or toddler having a meltdown

). Thus, such a comparison as a basis to the case to have pets in the resorts likely hinders the argument rather than bolster it.
In summary:
While I understand the premise to having a dedicate set of rooms for pets at WDW and the desire for pet owners to bring their pets with them, I believe the concept undermines the premise and specialty of Walt Disney World.
To elaborate, the resort IS a
safe haven for many families and children. WDW is a magical place where people with special challenges (be it mobility, socializing, allergies, age, whatever) can find a respite from their daily hyper diligence and have a
safe place to vacation. WDW is a place where families can
relax, let their guard down for a moment, and
enjoy their surroundings, knowing their loved ones will be treated well and not have a fear of something happening due to their challenge.
Introducing a pet resort (or even a hotel wing) has the real possibility to encroach on this zone of safety for many people. While service dogs are allowed*, they are relatively easy to spot and CM can be quick to intervene if something happens do to the dog's presence.
Thus, it is better from a business standpoint for WDW to remain pet free in their resorts, as it provides greater flexibility for them, reduces projected (and likely actual) maintenance costs, and allows all guests to feel safe.
*Also, the service dogs are allowed as their human masters need them, not because they want them.