It still functions just fine for such use, but if you live in a household with multiple iPhones, it can be annoying when you’re traveling alone with the pet.

If the device the AirTag is associated to is with you when you travel, it’s not an issue.

Hopefully associating AirTags to iCloud family is high on their list. There’s a lot of other cases where this is an issue (ex: using it on a vehicle fob/keychain that’s shared)