As for any "irrational irritation", there's not much I can offer.
Except that remember that this is a "game" and it is not attempting to be an "fortune telling device". In fact, in the sourcebook, it specifically says that the Sixth World Tarot isn't even a fortune telling device in the Shadowrun Universe.
Instead, it is a mysterious manifestation of 78 electronic devices that appear to have photographs of actual people in the Shadowrun universe in actual situations. What makes it unique is that the photos themselves should be impossible. Some of them are from impossible angles. Some of them are from private situations no one should even know about. Some of them may even be from the "near future".
No one in the Shadowrun universe has a complete "deck" of the Sixth World Tarot. They might have the one and only card of the "Three of Cups" in the entire world. Maybe they might upload a copy of the image to the Matrix - or maybe they won't. If they do - they might obscure it or modify it so that anyone downloading a copy will not have the full truth that's on the card. Rumor has it that the cards themselves have some ability or abilities to grant knowledge, wealth, and/or power, to whomever deciphers the puzzles within them.
Having offered that - maybe you can see it yourself to not think of them as "Tarot" cards like a neo-gypsy might scam a buck with, but are instead just another source book or game prop like a set of Weapons or Spell Cards.
Just a thought.