I would argue that service dogs, without question, apply to those considerations in the three other schools. This has been approved by various Muftis,
Seeing-eye dogs, dogs used for PTSD patients, have a significant purpose, analogous to guard dogs or sheep dogs. The issue for the scholars was having dogs as pets, which is considered very disliked, or makruh tahriman by the Hanafis, as enumerated by Sidi Fadi Qutub Zada, a view held by Shafi’is as well, while Hanbalis severely limit the keeping of a dog to only required purposes and thus rule keeping a dog without a purpose is haram.
Sheikh Muhammad Al-Munajjid writes:
With regard to the words of the questioner, “keeping a dog is naajis”. This is not exactly correct, because the najaasah (impurity) is not in the dog itself, rather it is in its saliva when it drinks from a vessel. If a person touches a dog or a dog touches him, that does not mean that he has to purify himself, whether with soil or water. But if a dog drinks from his vessel, then he has to throw away the water and wash it seven times with water and the eighth time with soil, if he wants to use it. If he makes it just for the dog then he does not have to purify it.
While Ibn Taymiyyah wrote:
With regard to dogs, there are three views among the scholars:
1 – That they are taahir (pure), even their saliva. This is the view of Maalik.
2 – That they are naajis (impure), even their hair. This is the view of al-Shaafa’i and is one of the two views narrated from Ahmad.
3 – Their hair is taahir but their saliva is naajis. This is the view of Abu Haneefah and of Ahmad in the other report narrated from him.
Therefore, to declare “dogs are haram” because some scholars consider them ritually impure is a ridiculous statement, for Ibn Taymiyyah writes:
"That is because the basic principle is that substances are taahir [pure], and it is not permissible to regard anything as naajis or haraam without evidence,"
Sheikh Muhammad Al-Munajjid, a Hanbali, wrote, when asked about a blind Muslim woman keeping a dog for her protection:
"…there is nothing wrong with this woman keeping this trained dog until Allaah provides her with a way out…"
I hope this helps, insha Allah.