Actually the last 2 allergists that we've seen have said the same thing about not making the decision to get rid of pets, and that was before testing. I'm sure it would have been different if we were talking about severe asthma and/or a severe pet allergy. Problem with most people is that there is not one trigger and it's impossible to get rid of everything a person is allergic to. Dust is a very common allergen and it's possible to take measures to decrease the dust, but there's not totally getting away from it. Of course it makes sense to eliminate the things that are possible to eliminate if the problems are severe.
I do think that it's easier to deal with a mild dog allergy than a mild cat allergy. Try telling my cats that they can't go into an open room. I don't think so...

However, we keep a baby gate closed to keep the dogs from going upstairs. Not so much to keep them out of the bedrooms, but to give the cats a sanctuary away from the dogs, but it does assure that the dogs are not in the bedroom.
Oh, and my son is older, with a very mild allergy. My son who had asthma doesn't have the pet allergies.