Secondary stats in this game are pretty boring, and everybody more or less builds for crit with a few exceptions/nuances. Here are some changes I think would be neat:
Critical Hit Rate - still effects rate and potency of crits, but affects the rate to a much lesser degree than it does currently (more on this later). Primarily for crit strength. Still affects DoT crits.
Determination - no longer effects any weaponskill or ability, only auto-attacks, but to a much greater degree than it currently does/ever did (triplefold or something like that). No effect on DoTs or heals.
Skill Speed - keep as is. Effects GCD/DoT damage.
Spell Speed - keep as is. Effects cast time/DoT/HoT damage.
New stat: Ardor - increases damage and healing dealt by all abilities, weaponskills, and spells. Has no effect on DoT damage or auto-attacks.
New stat: Acceleration - effects recast of abilities off the global cooldown. Cap on the possible reduction in recast time similar to the Spear card if enough of it is stacked.
Parry - effects parry rate and parry strength similar to how crit works. Also slightly boosts crit rate % of physical weaponskills and AAs only (since you parry with your weapon) and adds a bonus to the first instance of damage dealt after each parry (you parry 20% of a 1000 damage hit, next attack deals an extra 200 damage or something).
Accuracy - effects chance to hit and also slightly increases critical hit rate for weaponskills, spells, abilities, and AAs, but not DoTs.
Piety - Greater impact on MP regen in addition to increase MP cap.
Reasons this would be awesome:
Now there are incredibly varied secondary stat weights for almost every different job. Det is useless for BRD/MCH but Ardor is excellent. Parry and Accuracy have direct DPS benefits. Jobs with higher APM like DRG or DRK may prefer Acceleration and/or Ardor over other stats whereas jobs with few actions off the GCD like WAR wouldn't care. Crit not quite as powerful now, but still good. Crit and Skill Speed/Spell Speed still ideal for DoT jobs. Jobs that AA at an increased rate like PLD now value Det far more.