A headline would be used even if the car did physically touch the cyclist but hit the bike and knocked the off.

Also, we don't have headlines that say "bullet shoots child", because the person shooting the gun did not physically touch the child. In some of these cases, the car is the lethal weapon, the agency of person driving the car matters.

> but "driver hits cyclist" literally implies to me that one person punched another

"hits" can mean "impacted" or "run into", so it's accurate here even though it's not a punch.

https://www.google.com/search?hl=en&q=Christmas%20market%20k...

Most headlines were like "Lorry kills 12 at Christmas Market", like there was a killer truck on the loose.

Here's an alternate framing of an article where a car is a fatal weapon:

"Driver plows car into pedestrians at German bus stop, killing one" https://www.dw.com/en/driver-plows-car-into-pedestrians-at-g... The lead clarifies that "no assumptions should be made at this point".

It's factual that a man drove a truck into a Christmas market and another person drove into a pedestrian at a bus stop. That can be reported without an assumption of guilt without re-framing the story as if the cars drove themselves.