World of Warcraft taught us not to worry about money. You could take two gathering professions to make some extra cash, but by and large the game has made money less and less relevant in the grand scheme of things. Between daily quests, vendor trash, and the money directly dropped by humanoid enemies, you fund your usual kill-and-loot-a-thon through killing and looting directly. Half the times I would just sell even rare drops, because it wasn’t worth the effort of setting up an auction for the extra money.
Is there anything wrong with the model? Not at all. It facilitates the sort of game environment that the designers want. Money isn’t even all that valuable past a certain point, so giving players enough to spend feels reasonably generous. While that has resulted in some uncomfortable currency inflation, the bottom line is that it’s a valid model of running a game’s economy.
Enemies in FFXIV Gil do not drop money most of the time. The few that do drop piddling amounts. Nor does anything drop simple vendor trash; the only items fit solely for vendoring are the Allagan currency pieces, and those only come from chests and quest rewards. Rare drops are high-quality components, not weapons or armor. There’s no such thing as sidelining your gathering; gathering classes are, well, classes of their own, with unique mechanics and gear and so forth.
If you’re trying to make money just through vendors and killing things, you will be out of luck in short order. Heaven help you if you decided to aim for the level cap via FATE grinding, because you have no idea what money looks like. The gil rewarded for FATEs is just there to remind you that you’re broke.
Not that you can’t make plenty of money while still ignoring crafting and gathering. You just have to be smart. Scour the markets, see what sells, and start focusing on hunting and killing enemies that drop that. Be smart and don’t exclusively put up full stacks — there are a lot of crafters who just need ten Animal Hides and will pay a little more not to have a whole bunch of extra cluttering up the bank. You don’t need to gather if you don’t want to do so.
But you do need to do more than just sit back and wait for the money to roll in on its own. The game does everything short of popping up a message explaining exactly that. If you want to play a game wherein all you have to do is punch things to make money, you’ve got options out there already. This is not that sort of game.