Well actually my point does refute your reasoning you just don't actually want to hear it however if you need it more clearly spelled out for you I can elaborate.
As a main tank there is little to no incentive for me to run almost anything in the Duty Finder as it is seeing as the "adventurer in need" bonus is so insignificant it might as well not be there. In reality the case is that 9 out of 10 times if I actually need a dungeon for any reason (Ex roulette, Relic, WT) I can easily go solo, with people from my FC, my friends, or anyone from various Linkshells instead of actually using the Duty Finder if I really wanted to.
In the case that I need company seals however the DF is a viable option as I can go in as a tank and lot uncontested on tank gear which I can then turn into seals to be used for any number of things related to progression (crafting / relic). If i'm leveling a DPS and I need gear for that specific job then I queue as the job and roll the dice on the lots regardless of whether my competition needs it for seals, stats, or glamour.
The game itself has determined that the needs between classes are not the same given the ratio of DPS to Healer and Tank queues, you can ask anyone that has spent more than 5 minutes as a DPS class about this.
Why exactly are the needs of a NIN/DRG/MNK/MCH/BRD/BLM/SMN who doesn't want or is unable to tank or heal the same content equal when it comes to the same piece of equipment to a person actually performing those roles?
If anything why should that healer or tank now even bother doing anything in the Duty Finder as that role with random players if they don't even get to use the gear that drops for whatever form of progression they choose?
I can solo the majority of ARR dungeons as a tank already, why would I even bother using the DF as a tank for anything under Dusk Vigil if at this point it's now charity work because the game has decided that everyone has equal dibs on all roles gear even if they aren't going to play the role?
If you want a specific piece of gear for a specific job then by all means feel free to level (and play) that job in the content that drops it. Otherwise the freedom to enter the content as whatever you wish is the tradeoff you pay when it comes to lotting gear.