True, at times deer often don't pay enough attention when crossing a road with vehicle traffic.
However, in my experience adult deer appear to be hyper-aware when someone is moving through their domain (the woods, fields, etc) by foot, on bike, motorcycle, or other off road vehicle. I often saw them moving or running away but never saw one dart out of the brush to cross the path in front of me.
During mating season, when stirred up during hunting season, or otherwise spooked, yes, they are a real problem for those in vehicles on roads. Even in the middle of the day but especially from evening, through the night, and in the morning. In my experience, the hazard is both in rural and residential areas. (I've never seen one running crazy through the middle of a city but I'm guessing someone has.)
The bottom line is the same: A wise driver stays alert. A distracted driver may have an unpleasant surprise.
Once in Alaska I saw the aftermath of a collision between a bull moose and a jeep. Looked to me like they both lost.
JKJ