idk if it's been mentioned yet but pets DO have valuable uses in the game; yes.
Here's my ideas.
Yes, the bird pet would have a value in sending messages across the sea. whether it be a silly message or useful cry for help. Some people might say well why not use party chat? the issue with party chat is having multiple ships in one party becomes confusing to hear call outs sometimes.
dogs would be trackers for messages in a bottle, random chests spawns, washed up loot.
cats would be a mob confuser. This is to say that if a gang of skellys pop up the cat pet would distract 1 of the skeletons in the group for a set number of seconds, then proceed with a cool down.
Monkeys...well lets just say take the puke effect of blinding and change the color to yellow. In other words having the monkey pet would be useful during player combat. As a 1time use where giving it a banana would throw it to a player to blind them partially. The only way to refill it would be to give it a banana so it wouldn't be such an abuse during pvp.
In general all pets provide a npc partner during voyaging. 70% of my game play has been solo, so having even a pet would make my voyaging a lot more fun. Though if needed, there can be other uses in making them all do the same thing. (yet im not sure how a dog,cat,monkey could send messages to other crews.)