The game gives you exactly one tool to "check your dps", those are the various training dummies in the game. If you care so much about big numbers use those. Ultimately knowing the perfect rotation is useless if the fight is not going to give you 15 seconds to execute it.
The game is intended to be played by learning, you see a certain AOE pattern in a previous dungeon, then you see it later. For example those "columns" that people have to stand in that the current level 70 content is fond of? Those were previous Raid mechanics. Various AOE's in the HW content, were telegraphed in earlier dungeons. If you never did the Raid's, then those were new to you.
Even within the same dungeon, the earlier mobs and bosses telegraph what the final boss is going to do.
The game is not about who can do the most damage or who can do the trial the fastest, it's who can pass the trial, period. If the game creates incentives for big numbers or low completion times, then the player base gets even more toxic.
Hell, if SE wanted to teach players to be less toxic, they would adjust the rewards to greater if the boss gets to complete all it's phases. If you manage to skip a phase, or kill the boss so fast that the boss room doesn't get to close, then maybe that shouldn't be rewarded.
