Not true! For your first class, you should be able to get by on quest rewards (you should be able to get a new weapon and main armor pieces every 5 levels), and there are plenty of ways for a battle class to make money, whether by farming monster drops, earning GC seals or tomestones and exchanging for sellable goods, doing guildleves/guildhests, spiritbonding, or using duty roulette.

Secondly, crafting isn't free. Even if you gather all the materials yourself, that costs you time. If the time spent getting materials and crafting (not to mention the initial time cost to level the craft) takes more time than it'd take to save up the gil and buy it, you did not save money. This is what's called an opportunity cost, and something a lot of new moneymakers fail to realize.

Generally, I advise players to just focus on getting one class to 50 ASAP. This is mostly to focus on unlocks so they can start on endgame, as well as some unlocks like guildleves and ixali beast tribe quests that can help them level. Once they have their level 50 battle class, I'd say level all the crafters and gatherers, maybe even alongside their other battle class (they can all support each other). Again though, that's if crafting and gathering appeal to them.