Being adopted, I often wonder if that fear is one of the reasons I've never been sexually attracted to East Asians a day in my life.
I think the issue is really complicated and I can't think of a single solution that would make it better. What if you unknowingly slept with your sibling and got pregnant (or got your sibling pregnant if you're a male)? Checking DNA is taking safe sex way out there on another playing field. Also, there would be still be the freak accidents where a parent cheated or parented a child beforehand and never revealed it.
It's indeed sad. I imagine something like this would be very scarring