Cat owners have significantly lower cardiovascular deaths. Children growing up with a cat have an almost 50% lower development of asthma and allergies. They reduce stress and depression.

https://pmc.ncbi.nlm.nih.gov/articles/PMC3317329/

I think you'll find that's as true for animals who don't shed proteins evolved to elicit severe allergic reactions as it is for those that do.

Your reference begins with: "The presence of pets has been associated with reduction of stress and blood pressure and therefore may reduce the risk of cardiovascular diseases."