You know that annoying unable to install patch error with the FFXIV launcher? I think I found the problem...and a solution (it might not work for everyone). But it's a solution I haven't seen before.

Uninstall java, delete "My Games" folder from My documents folder and launch the game from shortcut, it went smoothly without problems....

Java probably has some security things that prevent the installation...
I hope this helps people, I've been reading people having this same problem for weeks and months...I also hope this helps Square enix fix this problem because you're losing really good people to this unable to patch error.

I'm not sure how you would uninstall java in ps4 but there might be some way.
Let me know if this helps anyone.