I haven't had much difficulty getting High Quality results while leveling crafting. I think if you're only getting a 1% High Quality rate while crafting, then you're probably doing something wrong. It just relies on getting most of the crafting classes to level 15 before taking any much higher than 15, so you get the cross-class skills you need. After 15, you can focus on just the ones you're most interested in, plus perhaps Culinarian, as it has a useful level 37 skill. (The rest will become important again once reaching endgame when you want the level 50 skills, but between 15 and 50 you can specialize, focusing on one or two at a time if you want.)

It's quite useful to be able to make your own HQ gear while leveling up. Sure, your battle classes can sometimes get better than HQ gear from dungeons, but only when RNG is in your favor and the right piece of gear drops right when you need it to. The rest of the time, when you haven't gotten a rare dungeon set lately, the best gear available is High Quality crafted gear. Now, those who aren't crafting can sometimes just buy that off the MB, but being able to make it yourself both saves some gil and guarantees that it will be available when you want it.

The crafting does take up time, though. If you're in a hurry to reach 50 as soon as possible, it's fine to level a single battle class first using a combination of dropped, quest, and purchased gear, and only then go back and work on crafting. It's just that you've missed one of the advantages of crafting by that point.