The reason that basically everyone will recommend going the omni route is that it makes everything easier. Cross class skills make completing high quality crafts easier. Being able to do your own sub-combines saves a ton of money. Knowing that if you need something you can do it yourself instead of finding a source just makes things easier. Without cross class skills you need to rely on luck more, on high quality ingredients more, and on out-leveling crafts more. If you cant do all the sub-combines then you might spend a lot of your potential profits on intermediary mats. Or failing that, you spend a lot of time trying to find people you can trade with(ill make you some ingots if you can get me some leather).

But can you single class? For sure. Just go into it knowing that youre doing it the hard way. And if you did have to pick one DoH class to do, Culinarian is the most independent. Very few of their recipes call for non-culinary crafted ingredients(as opposed to gathered ingredients which are split mostly between botany fishing and monster drops). And as for the question of doing just the gathering classes, you can absolutely do that. Youll end up buying most of your gear(either from players or npcs), but once you have gear a DoL class is set. Best of luck!