Besides operator responsibility, this is at least as much a design issue as anything else.
Put simply, the classic two-lane highway design isn't all that good.
Most of the accidents I hear about in rural areas fall into one of these categories: crossing the centre line (especially at night or in poor conditions), high-speed intersection crashes, crashes involving turning traffic (either onto or off the highway), hitting deer.
When there is only a centre line separating the two directions of travel, there is not much opportunity to correct mistakes. Simply widening the road by all of a metre and/or repainting lane lines to create a paved median strip just one metre wide and putting rumble strips along each yellow line would likely help enormously. It would also provide some space into which cars could enter to pass cyclists. In effect, you get many of the benefits of raised median without losing the flexibility and ease of maintenance of a single surface.
A third centre turning lane could have similar benefits, though one has to be careful that it wouldn't be abused and turned into a de facto passing lane. Nevertheless, it would potentially get left-turning cars out of the way and provide a place for straight-through traffic to pass right-turning cars.
Intersections should probably be gradually converted to roundabouts instead of wasting money on making signalized intersections in rural areas. Drivers need to be slowed down at rural intersections, and, if anything, traffic lights have the opposite effect by encouraging drivers to "step on it" to get through a long-lived green or a stale yellow.
And for deer, not a lot to be done other than more hunting and slower, more careful driving.