You're applying this to a serious crime, at least manslaughter if not murder. If prison isn't appropriate for that, what is prison appropriate for? I imagine an argument could be made that prison is never the right thing, but I don't think you're making that argument.
Harsher penalties don't always have the intended outcome, sure. But this isn't so much advocating a harsher penalty as advocating a penalty at all.
If I'm driving a car, what is my incentive to pay attention and try to avoid killing cyclists? Simple morals, obviously, but that doesn't work on everybody. If I'm a selfish asshole (lots of those out there) and I know I won't suffer legal penalties, why would I care about cyclists?
If you kill someone while driving a car and you are at fault, why should you not go to jail? That is the standard punishment in that scenario without the car, so why should adding a car make it go away?