That is PRECISELY why I ride 99% of the time on bike trails, nearly all of them in the "Rails to Trails" family of bike paths.
It's also why I absolutely LOVE Hilton Head!!! The entire island is honeycombed with bike trails. Hardly a day goes by when I am there that I am not out riding 10-25 miles.
Around here (Pittsburgh area), we are fortunate to have so many Rails to Trails. Apart from that, more and more communities (and Pittsburgh is among them) are providing more and more bike lanes with wider and wider borders and more and more protections (signs, cones, bright yellow lines, small barriers, etc.).
But I hear you. Whenever I have to ride my bike on a road without bike lane markings, I'm nervous. I have a rear view mirror attached beside my left handlebar grip, and I check it frequently.
Best of luck, King. Ride on... and stay SAFE!