It feels like promotion of virtue is a valuable social function and neither bigcorps nor government are incentivized or interested in doing it in the US?

Possibly explains the popularity of "12 rules for life" etc. Also I feel like it's an underappreciated theme in @balajis.eth's writings on network states.

Yes. Virtue is good because it’s decentralized self-control. The more virtuous the society, the more self-disciplined, the less need for centralized law enforcement, rules, and punishment in general.

Virtue is why we can have nice things.

Is there a distinction between virtue and trustworthiness?

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Hypothetically speaking, if you were to over-index on one (virtue or trustworthiness) in screening citizens for a network state, which would you choose?

Yes, eg. someone can be fully honest and trustworthy but still be lazy and eat unhealthy food every day.

Yes, I believe there is.
Virtue pertains qualities of good character of which I'd argue trustworthiness is one along with like kindness, courage and accountability. 
Trustworthiness pertains to reliability.

Aristotle: Virtue seeks the ethical mean; trustworthiness shows in reliability.

Kant: Virtue is moral duty; trustworthiness equals honesty.

Confucius: Virtue underpins morality; trustworthiness fortifies bonds.

Nietzsche: Virtue boosts power; trustworthiness depends on personal value.