It doesn't matter if whomever first came up with the idea of the Tarot intended for there to be a relationship between the cards and the Hebrew letters (and then Qabalah by association), because the fact is that by the time the decks were standardized, their format of 22 major cards, 4 suits, and 56 minor cards (1-10 + 4 courts) was a perfect fit for a visual representation of it, and anyone familiar with Qabalah can see that right away.
Now, as to the accuracy of the various interpretations of the Qabalah and their applications to the cards, this is spotty at best. In my personal opinion, Paul Foster Case was the most accurate in this association that I have come across thus far. There are some things that "fit", and some that don't, but for the majority of the things that don't fit, there are reasons for them that are laid out in the Sefer Yetzirah itself.
The decks that have this affiliation in mind are, I believe, an attempt to synthesize the various Western occult traditions (Qabalah, alchemy, hermeticism) into one setting, a setting that goes beyond normal language and reaches into the depths of symbolism, which would be understood by generations to follow as long as they were well versed in those traditions. One thing to keep in mind is that the ancient form of logic, as transmitted through the Sefer Yetzirah, Pythagoras, and Hermeticism, are really the source of all modern numerology and astrology, which are considered important aspects of the cards even by many people who know nothing about Qabalah or alchemy. You can choose to ignore this source and make up your own associations, but that is far from the spirit of the original system of thought, which is definitely a system with clear, discernible logic.
These are murky waters and you can't take any one person's interpretation of them as "the truth" (this includes the SY, since it is but a vestige in writing of a previously living spiritual process), but, you can learn a lot from the cards if you know what the symbols are pointing towards.