I'm no historian but as I understand it, the suits (as Batons, Cups, Swords and Coins) existed in tarot usage long before the elements (as well as the astrological and qabalistic correspondences) we use today were codified in the 19th century. As Nemia noted, the "implements" represented by the suits have associations beyond what the elements signify, although they aren't necessarily inconsistent with one another. Some inconsistency does arise when you try to bring playing-card suits into the picture, but they too can be reconciled. I blend the traditional suit meanings with the elemental overlay when I read. Not everyone is aware of the esoteric nature of elemental and astrological Fire, but they can relate to the more pragmatic Wands ideas of initiative, enterprise, ambition, desire and the possibility of risk-taking.