Some crimes do have intent requirements. First degree murder must be willful, deliberate, and premeditated, for example. So if you trip and accidentally stab someone with a knife you're holding and they die, that's not murder because it doesn't fit any of the intent requirements, and testimony about intent would be relevant.

But even with intent crimes, the ultimate reason for the intent isn't usually relevant. It's more about "did you mean to do X". The law won't punish someone for an involuntary action or an accident, only if someone chose to do something is punishment justified. But the reason for the choice rarely matters. If you intentionally walk into the road when the crosswalk sign is red then you're jaywalking and it doesn't really matter why. That sort of thing.

Voluntary manslaughter is a rare exception that gives an imperfect defense to murder for certain kinds of provocation, so we actually do need to examine the why there.