I don't agree. I'm not convinced threat of jail is an effective deterrent.
Do you think that about all crimes or just careless driving?
I'm inclined to agree that it is all a bit unclear whether imprisonment serves as a deterrant generally speaking. But if imprisonment is ever a deterrent, it's more likely to be effective on crimes like careless driving than it is for drug use or something (I think).
Edit: you've posted again and it answers my question, and fair enough, but you also say:
It didn't come from criminal intent.
I don't think that's necessarily relevant. The crime of careless driving is about a lack of (pre)meditation about what the driver is doing, so obviously there's no criminal intent - it hasn't even crossed their mind! Victorian mill owners didn't particularly intend for child weavers' fingers to be snipped off by dangerous machinery either. But at some point there is a degree of carelessness is that is so awful that it's appropriate to imprison someone for it, and that imprisonment should be used to send a message to "the community" along the lines of "hey, dickhead! ffs focus for a second and pay attention to what you're doing or you might end up in prison!".
Edit: as an aside, the CPS guidelines on this are worth reading: http://www.cps.gov.uk/legal/p_to_r/road_traffic_offences_guidance_on_prosecuting_cases_of_bad_driving/