Untrained humans are indeed terrible, but it's not hard to learn. The main problem is that most people don't shuffle long enough, or use shuffling methods that don't produce enough entropy.
If you use multiple shuffling methods, you can shuffle a deck reasonably well in less than a minute.
As far as I know, riffling and/or shuffling, palm to palm or on a table is fine.
Unless you assume the dealer can hide, move, or arrange one or more cards. But a cut is supposed to fix that.
A naive shuffle with a clean table and a clean deck of cards, in the dirt and dust sense, is to put all the cards face down and just smear them around with your hands, then collect them, and deal.
If you've ever bought a deck of cards, you know after a hand or two how well everyone can shuffle.
There's millions and millions and millions of possible decks, but a fair shuffle is practically guaranteed.
If you do a perfect riffle shuffle a standard deck 8 times it will return to its starting state, and people don't tend to do plan-to-palm shuffling enough to get a good random result.
If you combine the two, at least two riffles (though one or two more is significantly better) with palm-to-palms between and before, especially if the riffles are less than perfect, you tend to get a good random result (though obviously not cryptography-safe random).
That would undermine the result, but I'm not sure to what extent.