I believe jail time should be used not especially sparingly, but instead that prisons should be reduced in security and allow external jobs for low level offenses. Some people really do respond to negative enforcement, and having that in a humane way allows you to sentence people for lower level offenses, creating greater deterrence while still allowing them to continue parts of their life and importantly their jobs even through the punishment.

But traffic accidents against cycles are usually due to reckless driving. A driver is driving a multi ton machine, it is their responsibility to look out and be careful. Hitting someone when you fail to do so, is murder and should be treated as such. Reckless driving is driving with intent to kill.

Importantly, enforcement rates matter even more so than the actual punishment. No matter how strong the punishment, people will freely do it if they get off Scott free, so enforcing the law and holding reckless drivers accountable even without hitting people is an important FIRST step in stopping reckless driving. That means real punishment for running stop signs and failure to use turn signals, etc. but that requires police reform.

Throwing them in jail doesn't solve it. But it can make an example of them, and potentially reduce future bad drivers.