You have flipped the direction of the causal arrow here.
The existence of functioning and accessible court systems in the western world is one of the reasons that western societies have higher levels of trust—not the other way around. It's much easier to trust someone when you know that if they cheat you, you have recourse to pursue justice in the courts.
In my experience doing business in both developed countries and less-developed countries, there isn't much difference with regards to individual human beings' "integrity". In fact, in countries without functioning judicial systems, business owners might demonstrate more "integrity" toward their customers, vendors and partners than we see in the US—but this has more to do with incentives than it has to do with people's character. In countries without functioning and accessible judicial systems, people typically do business with people that they have done business with before, because doing business with strangers is so risky. Reputation matters a bit more.
> There's no technical utopia that will replace 'integrity'. Or frankly 'values'.
Yes, as a general matter, many of the problems that exist in the less-developed world originate from deficiencies of trust [0]. But again, this is largely attributable to there not being reliable ways for people in those societies to mediate disputes.
This isn't about utopia. If smart contracts can take the place of functioning court systems in commercial transactions—or at least can reduce the complexity of legal disputes and narrow the discretion of judges to influence dispute outcomes—a real problem is solved and an impediment standing in the way of economic development is removed.
Smart contracts allow for certain types of commercial transactions to be conducted without the existence of a reliable judicial system, which transactions would otherwise be too risky to undertake. This incremental improvement will have a material impact on people's lives.
[0] https://www.bi.team/blogs/social-trust-is-one-of-the-most-im...