I’ve had lovely exchanges with pets involved!
We’ve had dogs for decades - our dogs have never come along on exchanges. They have stayed with family elsewhere or at our usual kennel. We have looked after pets while home exchanging - cats and one time a rabbit. It was a lovely experience, and contribute a little bit to the changing of everyday life experience.
I do think it is important to acknowledge that the pets are always the responsibility of the adults. Some pets can be stressed by strangers or a lot of commotion. So it is not for all - not all pets - not all exchanges. I think, as I do for exchanges in general, that exchanging with similar families is an asset. It is also important to be transparent - also of the challenging stuff. This will get you a good match. It could be tempting to sugarcoat - yes, he is fully housetrained! when the dog is not, or being too accommodating. I’ve found it is best to be clear and accurate. “This can happen… then we do this”. If you miss out on an exchange by being transparent - well, better find out sooner than mid-exchange. Right?
The last year or so, we haven’t exchanged as a family, but I’ve been invited to look after pets as I travel. I have fond memories of my new friends with fur, also exploring their neighborhoods (with dogs - together!). Being a traveller walking the dog - it really connects you to the neighborhood. Nodding to the neighbor on our morning walk, someone recognizing the pet in the park. Or cuddling with the cat in the morning before heading out to a museum - then checking the time and seeing that you need to go home to your new friend for dinner. Spending the evening together reading with the pet at your feet. As a solo traveller it really is golden to have a pet away from home!