The PS4 isn't limiting the availability of an official parser, the community is. I still don't see why people are against it in extreme party finder content, as a flag the leader can set.
Yoshi-P did mention that they wanted to implement large scale FATEs where you'd fly onto the back of a beast and fight it with a huge amount of players but couldn't do so due to the PS3, very different from a parser as a large scale FATE like that would create new and exciting gameplay that's limited by the PS3. There's also armour textures, does anyone believe those are restricted by the PS4 when it can run the Witcher 3 and FFXV? Anyone remember the scene with Estinien and they zoomed into his shoulder only to reveal the PS2 era texture work on the "attachment" (trying not to spoil anything)? They could make separate texture packs for all armour sets depending on your platform, but that's a lot of work to consider especially with for a onetime close in scene. I do recall the PS3 limiting a glamour log as Yoshi-P stated that the PS3 couldn't load so much items in a listing, but that was most likely an excuse as is the multi-dye system being restricted by the PS4.
There's the cities being split in two zones, loading screens in some raids and dungeons, the lack of a number on the TP bar, lack of small detail in the over world (crates, grass, little objects, etc.) because those can't be disabled on a per system basis without a lot of work. A great example of the difference between platforms would be the difference between Dark Souls 2 and 3, Dark Souls 2 is quite bare on all platforms while 3 is filled to the brim with an immense amount of detail. All the flooring is visibly modeled and not a flat texture or an illusion with parallax occlusion mapping, there's breakable objects everywhere, highly detailed cloth physics and blood splatter and so on. You're definitely right about those small things being restricted by cost of implementation, but PS3 limitations and costs aren't exclusive.
Will it turn FFXIV into FFXV? No, but small changes would be appreciated. While I didn't play FFXI, I'd rather FFXIV not fall into the same trap and end up stagnating while slowly bleeding subscribers. WoW wouldn't be where it is today without constant updating of mechanics and visual fidelity and hopefully with the PS3 support being dropped we can get those eventual improvements.
Funnily enough, WoW: Legion has great open world content that's similar to FATEs but fun and interesting. I see people in the open world constantly and you can do the "FATEs" together without grouping up even. Unfortunately, Yoshi-P seems to take WoW's terrible and cheap ideas (time filler content such as garrisons) and ignore the good ones as they're too costly to implement. As for the FFXI team, I believe a lot of them do work for Yoshi-P now.