As far as I understand it -- pips and courts came first from the East into Europe -- 10 pips of four suits and 2 or maybe 3 courts (all male). Fairly early on in the west a female court was added, as an addition to the courts or a replacement for one of them. So the pips and various court scenarios were around c.14th century, and being 'allegorized'. In the first half of the fifteenth century the tarot trumps appear in the northern cities of Italy. It maybe that they were a separate game, that later was added to the 52/54 pack of cards, or maybe that they were created from the start as a 'trump' suit as an addition to the standard deck.
If they were separate games and subsequently amalgamated, then I suppose Waite has an argument. There is no doubt in my mind from the historical evidence that the trumps were a later addition--but maybe as much as the trumps were an extension of the game (pips/courts), they were as much an extension of the allegorical interpretation that had also apriori been applied to them (pips&courts).
I think that Waite is historically right in that they did not originate together, but that is different to saying they do not belong to one another--they make a perfect couple as far as I am concerned, and one that has stood the test of time. I have no interest in divorcing them. Whether by Fortune or Providence, they work together, and the minors IMHO are as meaningful both in an esoteric and exoteric sense as the majors. I'm not sure if it is a marriage of equals, but of the two, I am not sure which brings the greater dowry.