Games that sort the cards are the worst / most interesting for this. Gin rummy, etc, where the end result of a game is sorted groups of same-numbers and runs. You can really tell when then shuffling has just transposed a few cards.
There's the general belief that all magical tools develop significance for the user over time, something that my wife who is a "secular green witch" who doesn't believe in psi at all would tell you all about.
Scientifically though, if somebody isn't a good shuffler their deck is not going to be well shuffled and they'll get readings that deviate from what you'd get from a well shuffled deck. It's harder to shuffle a tarot deck well because it has more cards and these are frequently larger. (Personally my riffle shuffle is awful and probably not much better than an overhand)
A new deck usually has the major arcana together and in order and other cards might be sorted by suit and then number. We do a 5 card spread and if your have a new and poorly shuffled deck of course you are going to have more spreads where you get both the Emperor and the Empress or the 4 of Swords and the 7 of Swords.
I found the tarot readings were infinitely better to the person getting the reading when I just forced the results. So I did.
I still did all the things you're indicating about talking about specific personality, etc, as the patter to the concept.
I got into the tarot group because it's not so easy to find a therianthrope's guild!
From a scientific perspective there is a lot to say for randomness. Like the theory that the I Ching was a version of game theory from bronze age China. I recently created A System of Blessings with 13 selected characters from the I Ching because I wanted to give people something nice but didn't want to give everybody the same thing.
My job was to heighten their experience, and to essentially act as a mini therapist enabling them to feel confident in their own decisions.
But I feel you. I did things entirely differently to everyone else. Which is why I thought it was an interesting story.
Also see Magic players being fond of pile shuffles, which, of course, do very little randomization, and guarantee a good mana weave. Without a few shuffles of your own, most Magic decks ever presented are not sufficiently randomized, and it's even worse in Commander, where we are talking 100 card decks.
If anyone actually cared, and really learned the moves, it would be imperceptible, even on camera, but instead regularly players get caught doing the dumbest of obvious things, even while on camera.