Perhaps less worse, though not better.

Whether or not it is considered 'pragmatic' social contracts and natural rights are very flawed concepts. Appeals to nature, natural rights, Locke and Hobbes are fruits of the enlightenment that have gone rotten. Invocations of nature are easily dismissed and I think recently there has been strong criticism of contract theory, most notably those who have critiqued John Rawls' work. It is a problem of paternalism and consent (keywords if you wanted to do some googling), as well as the justification of the social contract (Leviathan and Rawls' original position).

I also don't see why it would need to be atheism, although I assume you mean secularism? I agree with your objection to the inclusion of religion within a constitution, that too is problematic.

All the best
- Kris Cussans