If i were redesigning tames, i would look at how they help you both on offence/defence and as a utility helping you progress into an automated base system.
The core concept of taming and riding is fine, but is pretty limited in its application in its current design. Part of the reason i love this game is that as you spend more time, you learn to become more efficient and progress your base/farming/ship building capability. At the moment farming on a tame gets you more resources, however we're now at a point where it feels like a grind. The 2x resource rates are fantastic, however it stops us from exploring as we feel like its wasted as we should be back home farming. In the early stages of the game, you are focused on harvesting basic materials to build up your base, and your basic ships for exploration and pirating. From there you start to shift to requiring gold and exotic materials.
I would suggest you implement a different use for NPC's, give them the ability to automatically harvest basic materials within your claim. Unlocking this ability will require a skill or by placing an new item in their inventory, you will also have to pay your crew so the requirement for gold should be able to help ensure that this is not just free resources. This should be an mid to late game ability that has risk and reward components. This would then change the way we run our bases, freeing up more time for the real game aspects, but still requiring you to design your base and implement defences from wild element and other players.
As for the tames themselves, give them a variance of passive buffs that can help you with either improve how you run your base, or how they help with offence/defence/exploration.
Add different equipables for tame, and please introduce a weight carrying cargo harness that allows us to put materials in.
Lotus’s post above has some amazing suggestions that align with the above.