I do think that our polity is more humane and - let's face it - legal since we have a vigilant press scrutinizing what our politicians and civil servants do. Very tempting otherwise to fudge and hope no one notices.
Transparency. Glasnost. Even if we'd have behaved properly anyway, better safe than sorry.
I agree, I'm very much with H.L. Mencken when he wrote: "Conscience is the inner voice that warns us somebody may be looking."
A functioning society and the expectation of being found out keep most people on the straight and narrow, from hunter-gatherers on. At the same time, most societies, I think all hunter-gatherer societies which have been studied, have some sort of belief in a spirit world, including expected retribution for sinful behaviour from gods or spirits or karma. We may even be wired up to expect this, and need some extra work to live without it? - like the inbuilt tendency to overeat sweet things, which were not common in the environment where humans evolved.
It can be disorientating for a society or individual to lose the belief in supernatural moral oversight quickly, there may well be a sense that all is permitted. The spread of atheism in Western societies has been going on for centuries, long enough to adjust, but even now it's unclear where morality fits in to the scientific world view, what the social and psychological mechanisms are. Like vision, they're probably more complicated than they feel.