It could, its just hard for the prosecution to handle. Because it's not direct evidence of the mindset for that incident and it's inflammatory to the jury the chances of it being ruled as prejudicial and not probative is high. That's why past criminal convictions are also often excluded from trials.

It shouldn't. I think people put far too much value on motive. Dead is dead. If I am killed by a gun or car it doesn't make any difference to me or my loved ones who will never see me again. Likewise, if I had a kid who was killed by a school shooter or someone who was gooning to his phone while driving, I would hate them both equally. Motive can't bring back the dead.

Obviously motive has some value, but it shouldn't be the difference between a few weeks of community service vs a lifetime in jail. Motive shouldn't have more weight than the actual consequences of our actions because that is insane and gives people this fucked up idea that they don't need to worry about preventing the deaths of others as long as they don't intentionally kill anyone they can drive like the most selfish asshole in the world and they will never go to jail