Every Animal should have a purpose. They shouldn't just exist as stepping stones to other creatures, in addition the once that are mounts should have a type of gathering ability. Going through the list, there's still a few animals with little purpose. For some reason the herbivores are bad at thatch and bad at wood by default which makes Thatch very difficult to harvest. First off, upgrade the Cargo Saddle to carry things. There's multiple ways to do it, choose whichever is easiest. You could have it upgrade the animals carry weight straight up, or it could be a new placeable item. One that reduces the weight of things inside it, and allow it to be placed on the cart where only gun mounts and cannons can go at the moment. You could also go more complicated and let it be a 1x1 floor and build on it like ships and have even more options but that's unnecessary.
Tier 1 Riding: Fix this. Right now only 1 creature can even use a tier 1 saddle, sheep. It's a useless item.
Bull: It can breed with cows. That's about it. Let it pull the Cargo Saddle, and also make it a multi-purpose gatherer. Give it a medium amount gather for Fiber, Thatch, Wood, Flint, Stone, and Metal.
Horse: The bear does everything it does better except for running speed and turning ability. I suggest making them easier to tame and add the Lasso back in. If the Cargo Saddle is upgraded then it'll be good. Let it use a tier 1 as well as tier 2 saddle. Also, saw a great idea others had. Add its damage bonus to the melee weapon that the rider wields to Pseudo simulate the cavalry charge.
Ostrich: Make it easier to tame like the horse. Any animals that are mainly for travel should be super easy to tame. Like the Bull/Horse let it use a tier 1 as well as tier 2 saddle
Wolf: Too weak. Make it easier to tame and then give it a pack buff like the Allosaurus. Alternatively, it could also be cool to have a sort of herding power. Give it a command to keep Sheep, Cows, Pigs, or Chickens within a certain range of it. The only problem is we'd also want the herded animals to stay group up tight, so a 'go to' command for animals of a certain type could do it.
Penguin: Make the insulation work on baby animals.
Giraffe: Give it good thatch gathering, having a tall multi mount is pretty useless. The elephant can seat more, carry more, and actually gather/carry wood.
Rhino: Need these to stop disappearing into the ground because of their huge and unusual hit box.
Last off, it would be nice to encourage the animals that humans actually used. It would be nice to see mostly the animals we actually tamed being the mainstays of player use. Chicken, Sheep, Horses, Cows/Bulls, and Pigs. They should all get reduced taming difficulty(faster progress, easier to bola), as well as much faster maturation times for breeding. If they're very easy to breed it would make sense to just make tons of them rather than having to tame every single animal from scratch. Having many of them would make them less valuable and more widespread, it would also make it more convenient to breed them for food(which only the chicken/cow fulfills atm with eggs/milk).
