As a frequent flyer with a pet allergy, I think Alaska's handling of this situation was pretty normal - most of the time when I have allergy issues, UA/AA/DL have not been willing to move the pax with accompanying animal, and instead reseated me to the last rows of the cabin. Once or twice, I've even had to get rebooked, which is frustrating but sometimes the best alternative. Prioritizing people with pets (in particular ESAs/"ESAs") over people with allergies is coded into American laws, and there's not much airlines can do about it.

My worst flying experience with an animal on board was flying T5 from ASB to DME - an old Russian lady had brought a cat in a bag, and even moving to the back of the cabin didn't help with my allergies. Unfortunately, I didn't have the time to wait for the next flight 3 days later and didn't have the heart to try to convince the airline to make the lady wait, so I suffered through the 3 hour flight and took lots of allergy medication.