Alright so I've had a handful of ideas that I'd really like to see and I figured I might as well post them here. I know there's floods of suggestions and SE likely won't see them all, but here goes nothing.
Expansion of the companion system: This system has so much potential but has been left on the floor too long. Adding a member of a maxed beast tribe as a selectable companion to level. Any notable npcs (i.e Raubahn, Thancred, etc) to call upon. The higher the level, the better the bond. Maybe have bond quests that teach them skills. Completing bond can give you a unique reward or title or both. Possibly adding companion based dungeons that are like solo versions where you use your companion.
Customizable adornments to armor: Example being a crafter can attach a design on a piece of gear like a sigil, crest, or pattern that can be dropped from dungeons or crafted. These designs can be dyed as well to give that BiS armor everyone is wearing more uniqueness.
Add FFXI style fishing to FFXIV: In ffxi when you fished you had to deplete the stamina of the fish and it almost felt like you were actually fighting with the fish to get it. Right now it's just as simple as hitting reel in to get it. I feel maybe people would like fishing more if it was more interactive.
SMN ability that turns the egi into the primal for a short time: I hate the small egi's, i do. One neat idea i thought of without making a giant primal follow around a smn is an ability like enkindle, invokes the power of the primal to the egi. Maybe makes the smn unable to use anything during the process, but turns the egi into the actual primal/visage of for like 30seconds, doing some serious damage.
Other job specific mounts: Honestly I know tanking is annoying so having the reward is cool, but I think each job deserves a job specific mount, even if dps have to do more expert roulettes than healers and tanks.
Gathering fields for Free company: Like buying a house, or making an airship, I think a fantastic addition would be for a Free company to purchase land for resources, the more points spent could allow for the land to grow and produce greater gathering points. Allowing for gathering points only for those in the free company.
Speed/Solo challenges of older dungeons: Adding achievements or rewards for soloing or beating older dungeons or trials. Most likely just titles, but maybe a reward after completing all.
Support Job Role Slot: I realize this would completely change the system and so it'd be highly unlikely, but I always liked the idea of steering away from just the trinity.
Co-op Emotes: If you use the emote itll prompt your friend to reciprocate and then the co-op emote will take place. (I.e piggback rides, lalafells sitting on shoulders, arm wrestling...)