I'd rather the "mobile app" already designed, not overlap with the game client functionality in a way that would cause the developers to have to maintain two or more things.
What Kurando is mentioning is that the "launcher" is part of the game for Diablo, which it's likely not. There is a simple reason for this that goes all the way back to pre-Windows time called "File Sharing" in the original context, which means that if one file is open for reading, another program can not write to it, no matter what. So in order to patch a game, two steps are required, one a launcher to do the patching, and another that is the actual game client.
What JP/KR/US/EU games do is they put the launcher and patcher into the same program, which wraps the web browser (everything inside the window is actually HTML) all the "program" part does connect to that address so that it does the user authentication. The backwards part that SE does is not downloading the patch BEFORE connecting. But they might just do that to prevent people from trying to download patches before the servers are online, because that's exactly what people do with new content. With games/expansions not yet purchased, you don't want people finding a way to exploit that either.
In V1.0, and still now, there is the FFXIV Boot program. This is actually the "launcher/patcher" for the Launcher itself. This program simply contacts SE and goes "What is the latest version" and if if the version mismatches, it downloads the current version of the launcher. It did it this way at V1.0 which the V1.0 launcher contained some level of P2P patch downloading in it. At least that's what I recall. The current patcher's use a CDN to download as far as I know. So largely there is no reason for "boot" anymore since the launcher could simply use the same mechanism existing programs use to self-update (eg download new version, launch installer in "unattended-wait" mode, exit old version, new version overwrites old version, re-opens. You might see this when you launch Steam.
Which leads me to the other point, the Launcher is necessary because of Steam or any other "service" needs an authentication program to actually launch, and a Steam version requires linkage to the Steam API. However if you've played any MMO on Steam, you'd also notice that every game with multiplayer functionality has this second-launching mechanic as well. A player may obtain the game from SE directly or from Steam, or for MacOSX, the launcher launches the same program no matter what way it was purchased. Otherwise Steam would need to integrate every publisher's authentication system, and that's just not reasonable at all. Even the oldest MMO game I've played that put a version into Steam, all Steam does is "patch" the base game. The launcher still does the authentication, it just doesn't need to do a second round of patching.
Blizzard-Activision doesn't play nice with Steam (You'll notice that zero Blizzard titles are on Steam, or anywhere else for that matter) their battle.net App is designed to launch only their games, so it really just copies functionality that Steam already had.
One very minor thing I want to point out, that isn't obvious unless you've been playing MMO's since before Windows Vista, the one thing the launcher serves as in Vista and later is to reduce the number of privilege escalation requests. When you run something like Steam or Filezilla, when it self-updates, you typically get a escalation request. Where as the launcher is already whitelisted, and thus has the write privileges it needs to patch the game and launch it without a multiple escalation requests popping up. Which can be bad if a patch is really really screwed up.