I like the entire therapy animal or emotional support animal movement. While not covered by insurance, they also don't charge per hour. Tough to travel with them on an airplane, as evidenced by the person whose therapy squirrel got her kicked off:

Passenger who brought emotional support squirrel on flight speaks out

Same with an airline passenger's emotional support peacock:

United refused to let an emotional support peacock board plane

And a fun blog post with pictures:

10 Weird Emotional Support Animals You Don't See Everyday

I'd be thrilled to find a turkey or a miniature horse with the passenger next to me. I love animals and I think it would make flying more interesting. They probably smell better than some people I've sat next to on planes, too, including my kid, who has puked on my H a couple of times.