A couple things are important out of the gate when discussing this issue. The first of which is to question why you want 370 gear in the first place. Ultimately SE has decided 350 gear is the minimum Ilvl needed to reasonable complete 08s and this is achievable in 4 weeks of Sigma normal + mendacity. If you have no desire to attempt these fights or do not find them enjoyable, simply do not partake in them. The gear you have now is likely more than enough to challenge any other content.
If you want to focus on the progression, remember there is a lot of horizontal progression too. Crafting, gathering, glamour, various collections, and housing to name a few. Your character is not finished when you are done normal PvE content unless that is where you choose to let it sit. If none of these things interest you then imagine you clear God Kefka by the next raid tier. What is your goal then? Item level is nice but its a finite journey and the work you put it gets replaced often. If you take defeating content as the goal instead it'll make the gear grind a lot less painful.
Parsers certainly exist in the game but they are not the only way to tell if you are playing competently. If you kill the respective savage dummy in the allotted time you can feel confident that you can kill that boss if you can maintain up-time or follow mechanics. Of course DPS checks have to exist otherwise there would be no point but to take 6 tanks and two healers to trivialise incoming damage since you have infinite time. DPS checks usually aren't tough to beat. Play competently and don't die for 10 minutes. If 8 people in a party do that it results in a clear, even in savage. While that is a lot to ask of pugs, many people pug the first two savage bosses every day and some clear the third with a few even pugging God Kefka himself. Maybe you got unlucky with your groups but I know from experience savage bosses can be pugged. The content is designed to make the first two relatively easy while the third and fourth both take massive steps up.
You called yourself bad, I don't want to be insulting, but you should question whether or not you deserve to be geared just as well as people who put in the time to get good at the game. Savage content is reserved for people willing to challenge themselves a little. 370 and ultimate gear is the reward they get for putting in that time and testing their abilities. If there was no challenge to this final step then what would even be the point of gear? Why get so many stats when none of it matters? You cant completely blame pugs when many fights end up being pugged and there is always the option to look for a soft core static. If you can't call yourself good, why do you deserve to get anything anyone else has when they put in the effort?
You say you cant think of an MMO that's been this infuriating but look at WoW. WoW is often described as the game with the best raiding of any MMO despite what ever flaws we may say it has. It wins out by experience in this field in most cases. Due to the prevalence in parsers and UI add-ons, healing and DPS checks are way tighter than anything this game has offered so far. I hate to say this but if you encountered all of these issues with XIV, you may not be cut out for theme park styled MMOs.
A bit of advice on progression would be to work on a job until you feel like you are really doing well on it and then rethink this thread and the challenges you've faced. Im sure it'll make a difference on your outlook and do far more for your DPS then one or two 370 pieces.