I don't think there is a way to fix parry. It's an antiquated stat that doesn't work in FFXIV. Any change you would make to it would basically be a complete rework. This is probably why they are tabling any changes until a later time when they have more options to address it.
The problems really boil down to a few points. None of these points are really related to the effectiveness of parry.
The first is that it's a passive mitigation stat. As such, it's boring and flavorless. Many game developers have come to this realization regarding passive mitigation and instead opt for active mitigation. To be fair, SE has tried to make parry a more active stat by tying it to skills like reprisal and lowblow (and they made another passive mitigation stat, block, more active through shield swipe). And, when I play DRK, I do genuinely want a parry to occur and feel excited when one happens. The obvious issue is this dynamic is exclusive to DRK and the stat itself is still devalued by dark dance. For PLD and WAR it's still a really boring stat.
Just to prove a point, imagine if every time a WAR parried an attack, it activated fell cleave for a short window. Parry would instantly be every WAR's best friend. They need to find a way to make parry an active stat for every tank class. That said, skills like raw intuition heavily complicate this task.
The second issue actually runs in opposition to the last point which makes parry such a complicated design problem. Even if you find a way to make parry a more active and engaging stat, it's still only relevant while you are getting hit. SE designs fights with forced tank swaps and split MT up-time. I doubt this is going to change. When a stat is dead weight for larger portions of every fight, it's a little hard to justify its value. As such, it becomes difficult gating any real value behind parry because it only serves to widen the disparity between MT and OT effectiveness. We already have DRKs lamenting their lack of utility when OTing and the tanking trinity suffering from the pigeon-holing of tanking roles based on their job. It doesn't need to get even worse.
So I think SE will probably be looking at the versatility of the stat, its relevancy across different content and roles, and how engaging it is.
Personally, I think they need to take a long, focused look at WARs and realize they hit a home run with their design and base everything on them. For example, vengeance and raw intuition are defensive cooldowns that still retain some value even when you aren't taking damage -- and rather crucial value because they allow WARs to triple FC. Parry needs to work in the same way. There needs to be some way to funnel the stat into a different, equally impactful function while OTing just like how WARs can repurpose vengeance and raw intuition as ogcd stack generators. Maybe you go with something straight forward like funneling parry into crit / det while in SwO / deliverance / blood weapon are active.
After you make parry a valuable stat even when OTing, you open your options for increasing its impact while MTing. Perhaps while in Defiance every parry has a chance of generating a stack of wrath. Perhaps for PLD a parry will remove the GCD cost of SwO or activate RA much like a block activates shield swipe. Maybe you buff reprisal, low blow, or give DRK some more parry gated perks.