I can't imagine too many cyclists being a problem on tour in any but a VERY few times and places. On the most used AC routes you might bump into a few cyclists per day at most. The one exception I have seen was the Pacific Coast and that mostly only because there was an organized charity ride that was on approximately the same schedule as me.

Off of established touring routes if you run into a handful of touring cyclists in a week it is a lot.

The dangers you list seem pretty far fetched to me. I wouldn't give them much thought. Relax and go touring just about anywhere that seems appealing to you.