Unfortunately, that is not scalable. Even within academia, there is a lot of proof of work going on, it is a very natural phenomena if you look deeply enough. Consider some area of academia, you have to come up with a hypothesis, test it, collect data, analyze it and publish; your peers will review it and verify/refute it, there is no "top down" acceptance of someones word on face-value (if it is, then it is not science).
No, you're misunderstanding what the term 'integrity' means.
The notion goes far beyond narrow views of 'scientific reasoning'.
Integrity, far from 'unscalable', is an essential factor in the functioning of civil society and probably the #1 predictor of a successful ongoing civilization.
The difference between a rich and poor country is sometimes 'natural resources' but more often than not highly organized social order based around institutions and systems with integrity. In everything from 'Sushi Chef' to 'Parenting' to 'Early Childhood Education' to 'DMV' to 'Drug Regulation' and 'Accounting Principles'.
Sure, locally, those principles work, because you see and interact with the people often. But on the internet, it doesn't work, that's where I was going with "unscalable", I'm not claiming that you have to ditch "integrity" for something else, most of the large scale human endeavors can't just rely on integrity (on that large scale).