I'm unsure if I'm getting requests to join my Alliance from players flooding alliances with requests or the game allows players to request to join alliances while they're in an alliance. But, it would be nice if we could invite players who are already in alliances, as it gets frustrating when players request to join and when you invite them, the game tells you they're already in an alliance.

If the game allows players in an alliance to send a request while being in an alliance, this is an oversight.

It's possible this cannot happen. I know in FFXIV, if you send an application to a Free Company (their guild/alliance system) you actually are temporarily part of that FC/guild/alliance until you withdraw or are denied. I've actually purposely done this to avoid people sending me FC invites randomly, as I would rather ghave people tell/whisper me and put effort into getting me into their place.