As far as triple triad goes, I'm not surprised it was designed around grinds.
I mean, let's look at it as a base concept. Triple Triad is a side-activity that's designed to take a while (even as far back as FFVIII it would take you a while to get 100% completion on all cards, not including the questline to beat the king of cards). Mechanics-wise it's not a game that has standard units in a matter of speaking. It's not like blackjack or old maid or trumps or go fish, which are limited by a standard 52-card deck (meaning you can play as long as you have a 52-card deck). The more "strong" cards you collect, the bigger your chances of winning. And as is common with collectible card games, it becomes less a game of luck/skill and more a game of what deck you choose to play with.
Since your deck has such a strong effect on your chances of winning, it is logical to make that part of TT take time to achieve. In addition, unlike FFVIII and FFIX (which have a finite number of assets), FFXIV is constantly growing due to being an MMORPG, so its longevity has to span beyond what we saw in VIII and IX (read: more assets in-game = more cards = more time involved in completing a collection and putting together a deck). Atrophy happens to be the antithesis of collectible card games (hence why Magic: The Gathering and Yu-Gi-Oh revise rules and constantly add cards), so making it finite would go against the whole point of a CCG. Likewise, CCGs by nature take a loooooooong time to complete a collection (this is why you see rare cards going for ridiculous prices in comic book shops and e-bay).
tl;dr - Triple Triad is designed along the lines of collectible card games in real life, and as such will take a long time to collect cards.