Parry was way, way worse than tenacity. Parry didn't do anything for damage increase (well, except on DRK, but even that was about 0.1% or less), was useless on crit hits, blocked or magical attacks, and was fully rng-based, similar and worse to crit. Crit at least increases your damage done + rate, parry just increased the rate, and iirc parry also scaled worse than crit.
Tenacity affects all incoming damage, as well as increases your damage equal to 67% of determination.
Yeah, you want to avoid getting tenacity for dps purpose. Heck, even the recent world first and second on Alex Ultimate didn't meld tenacity or prefered tenacity gear. Yet, it's still far from useless. And even a tank focusing on tenacity isn't much of a burden to the party, their damage 'loss' is mostly neglectable. Parry on the other hand... is like playing tank for the most basic tanks' sake (<- don't do this!)
edit: Skill/spell speed is in a strange position. It is indeed better getting a certain tier from it, so it'll end up being an increase. (Or so it seems)
Yet, it doesn't increase your ability damage or recast time, it only affects your GCD actions, (dots from abilities) and auto attacks, and the later is pretty much useless for casters with the exception of SMN 'cause of their pets (correct me if I am wrong here).
And because of that reason will end up being more of a loss than an increase in most cases. Jobs that benefit from it more are SAM and MNK with Haste buffs, but even then it only goes for certain tier and more of it end up being overkill, useless or rightout even a loss by screwing up the rotation and buff windows. E.g. SAM doesn't want any GCD faster than 2.0s.
I would argue that SkS/SpS is even worse than tenacity. Someone on balance discord created a slow GNB build that is on par, or better than your average 2.4s GCD build, despite the fact that the 9th GCD in No Mercy window wouldn't be buffed. And it works because you don't clip your oGCDs, and your abilities are way more buffed by increased det/crit/ten value due to decreased SkS value.