I have a pretty unpopular take on this, being married to someone with severe pet allergies. That take is, dogs (and cats) have no place on an airplane, and responsible adults shouldn't get pets that they can't find sitters for or board while they are away. Planes are enclosed-air spaces, and the allergens from your dog make anyone with allergies miserable for the entire duration of the flight. Every single time we end up on a plane with a dog (even the "hypoallergenic" ones), my wife ends up sick. Not to mention the fact that there are plenty of people with severe phobias of dogs, and that the animals themselves tend to be extremely uncomfortable on flights. That last factor has actually led to a number of innocent people sitting next to folks with dogs getting bit, etc on planes.

Actual service animals do still belong, because they provide an actual service, are extremely well-trained, and are worth the allergen/phobia tradeoff because folks who need them literally need them.

The amount of entitlement that pet owners have to impose the downsides of their pets on others boggles my mind sometimes.