Finally, paternity tests are useless in the presence of identical twin men. A twin is not responsible legally for the children of his twin brother. What matters is who had sex with the mother. Any system needs to have ways to solve this.
Personally, I think we should look towards the most well-tested paternity system -- marriage (and the accompanying social stigma of adultery) -- for advice on how to move forward. Paternity tests can be a part of that, but they are not the panacea you make them out to be, including relatively common situations.
> Paternity tests are accurate, but they are not 100% accurate.
I think most people would consider the problem solved if they were 99% accurate. Also, like all medical tests, a adverse result would require further follow up for confirmation to rule out potentially confounding factors.