I don't think that has to do with predators, not directly in that way. Imo it's very important for rabbits to be able to move, to know where they are and to know where to go at any moment. They have their paths they bolt along when needed, they always know where those are and how to get to safety. Picking them up, holding them, carrying them to and fro restricts their mobility and orientation, which is the same as safety for them, they don't like that. And some just don't like being held, or even touched (like my 8yo spayed Red)
Domestication worked on that issue partially, some rabbits cope better than others, that's a personality thing, and it can be trained within that frame, at least that they calmly accept it (patience, small steps, and treats). The true personality shows when they grow up, I would say around 6 months, but I can see tendencies in younger kits already, who is skittish or a daredevil.
Has nothing to do with spaying or neutering, it's just not a rabbit thing. it's like it's not a cat thing to learn tricks, can sometimes be done but isn't the rule.