I could imagine an overhaul of the animal training system based on fields and gradients rather than on/off switches like it is now. Rather than a TRAINABLE boolean, they could have stats for Intelligence, Aggression and Empathy that vary by individual and are passed on genetically and determine what kind of training they will be best at. For example, a Lion is very aggressive, but has the capacity for empathy because it is a social animal. A python is not very aggressive, but also completely lacks empathy. In the real world, the docile attitude makes pythons potential pets, and the lack of empathy is not a deal-breaker, but prevents them from becoming 100% tame. A lion's aggression combined with its size make them way too dangerous to be pets, but their ability to empathize makes them capable of being trained for circuses and movie work, and allegedly for war. Note that a housecat is probably as aggressive as a lion and less empathetic because they are solitary animals; we get along because we mutually benefit from interaction which is why cats ADOPT_OWNER. Birds like parrots and ravens are not particularly empathetic, but can be trained because they are very intelligent.
Anyways, the interaction would obviously be simplified for Dwarf Fortress. An ideal mix of Intelligence, Aggression and Empathy will allow the animal to be 100% trainable, like a dog, while other mixes will allow them to be partially% trained which may result in them attacking dwarves, running away, stealing food or damaging property. Being trained as children would increase the maximum % trainability but not guarantee 100% domestication like it does now. Instead, the balance of Int, Agg and Emp would be passed on genetically and you would try to breed the perfect animal.
So if you find an animal you want to conscript, you would catch 'em and raise 'em until they got smart enough to tame. Animals like say a giant bug might be so dumb, aggressive and unempathetic that they would require 100s of generations to be bred into something remotely trainable.
And even if that system gets implemented, we'll complain that such and such an animal is smarter or more empathetic than toady decided it should be. I in particular worry that crocodiles would be labeled as stupid and unfeeling, whereas my impression is that they are not much worse than cats in the departments of Intelligence and Empathy, but wildly more dangerous. If a cat were as large as a crocodile, it would probably try to eat you too.