I don't think we're talking about electronic documents in general. Electronic submission and eSigning of documents exists in the federal government and in many states. Tax returns, court pleadings, entity formation documents, real estate deeds and mortgages, etc, etc are, depending on the state, capable of being signed and filed electronically using accepted verification procedures.
What we are talking about in the case of pilot and medical certificates is nothing more than the digital equivalent of a photocopy. I would not expect a LEO pulling me over for a traffic violation to accept a photocopy of my drivers license. The issue is visible authenticity. For example, my driver's license has watermarks that would not appear on a copy or be difficult to counterfeit. I would expect states going the digital route for licenses and certificates that need to be carried on one's person to have similar methods of immediate verification, not only by LEOs but by the guy or gal serving you drinks at a restaurant, bar or sports arena.
I don't doubt there are those who would accept a duplicate and there is probably no reason why an FAA certificate or medical "needs" to be an original. Heck, with nothing more that a photo ID, they can just look you up and verify you are a pilot and have a medical. But in that case, there's no need to a duplicate either, right?