Issue 1) Please change your requirements for downloading patches.
Currently, the rule is that we have to log in, proving that we have an active subscription, before we can start downloading a patch. I think it should be based on having purchased the software rather than on having an active subscription. For one thing, it just makes more sense for downloading the software to be based on purchase of that software and access to the game servers for actually playing be what's based on having an active subscription. But the more important reason is because of updating services.
The Playstation Network has a feature for Playstation Plus members, that their PS3 or PS4 will periodically (once a day at a time of the user's choosing) check for update patches of any games registered through PSN. PC games typically use a similar service that runs in the background and checks in with the patch servers periodically to see if there are any new updates, and initiates a download whenever it finds one.
The PSN's updating service does not work with FFXIV, however. (I don't actually know about the PC version, though I'd suspect it lacks the same ability.) I think this is tied to the fact that we have to log in before the launcher will initiate a download. This means downloads cannot happen while we're sleeping or away at work. They have to happen when we're there to log in. That's not a good time to start a download. We're typically there to log in when we're available to start playing, and it would be better for downloads to use the time that we're not there.
There's also another (perhaps more minor) issue tied to logging in before we can download updates. It means that players whose subscription has lapsed but who plan to come back to the game eventually cannot keep their software up to date. So once they finally do renew their subscription they cannot start playing, but have to spend the first day or two of their subscription time on downloading all the updates that have occurred since they were last on. The longer their lapse is, the bigger of an issue this gets to be, and it can eventually create a disincentive to re-subscribing.
Issue 2) During patch-related maintenance windows, please update the patch servers first.
This issue doesn't really apply so much to the sort of minor patches we get with hotfixes, but whenever there's a large patch with a long maintenance window surrounding putting it in, please prioritize the maintenance window work so that the patch servers (and any networking equipment for reaching the patch servers) is completed first, before the game servers. Then allow access for players to begin patching their software while you continue any work that's needed on the game servers.
(With this last maintenance, I tried logging in late last night to see whether I could get the download running while I slept. It was 22 hours into a 25 hour maintenance window, and I still couldn't log in to download. Obviously, the game servers themselves would still all be down at that point, but it seems like after 22 hours, you could have at least gotten the patch servers back online.)
Of those two issues, I think #1 is the most important, but #2 could provide a nice QOL improvement. Please consider both.