Fang and Claw/Wheeling Thrust exist as our positionals (not that positionals are particularly interesting parts of the game, should just be removed) and also serve to make our combos round out nicely. Without them, we'd be doing Chaos Thrust x1 Full Thrust x2 instead of doing them back and forth. Both Fang and Claw/Wheeling Thrust also give us something to use that extra Life Surge on in the opener. I get why you feel like it's arbitrary, but I honestly feel like a lot of how the job's combo works feels arbitrary. The DoT and Power Surge feel inconsequential since you just refresh them by existing.
Mirage Dive does in fact give you some choice, allowing you to choose to delay Life of the Dragon and better align with raid buffs. Geirskogul doesn't give us any choice because we need to use it on cooldown, same with High Jump. So Mirage Dive being there to allow us to choose when to pull the trigger on Life of the Dragon grants Dragoon at least a bit of flexibility in its rigid rotation. I do think they could handle this better of course.
I don't think that DRG's rotation is particularly interesting. I think it feels nice even if it's braindead, and it's good practice for maintaining uptime if you ever wanted a job with transferrable skills to other ones because it's the most straightforward melee DPS currently.
Personally, I think they need to tear down how its GCD rotation works currently, and rework it. Something like this:
This is really just an off-the-cuff idea, but I think that something like that could grant the job more flexibility and reduce button bloat. It also gives you some choice in AoE situations since currently you just press 123 over and over again with the occasional Wyrmwind Thrust. You'd have one simple combo that leads into different finishers, and it places an emphasis on jumps without it being "press every jump on cooldown".
I think that the job feels clunky because its abilities don't interact with each other in any meaningful way except for the interaction between High Jump and Geirskogul. They do stuff like make WAR's Upheaval and Inner Release independent from each other, and remove its crit buff from the gauge which all amounts to making the job a "press stuff on cooldown" job. Dragoon is and has been this way for a long time as well, and I think that RPR is a step in the right direction because besides trying to make sure it can burst every 2 minutes it does feel a lot more simple, smooth, and flexible. DRG and NIN feel so dated and clunky because it feels so rigid and restrictive to play them, while somehow lacking in nuance.