Who knows? But they obviously have some sort of reason. Maybe they actually rent server space? Something like cloud storage? Hard to say...
If SE ever tells me, I'll let you know. :P
Except it is a restriction, and alts will allow a majority of players to get around it. Yes, you're right in that it's the same inventory slots per character. If one were to play each character just as often and collect a similar amount of items on each, then the inventory space will be filled with each own character's stuff.
But let's face reality: most players won't be using those alts for that. Let's say alt mailing was introduced. Those who only play one or two characters will suddenly make 6 or 7 more. Just like in every other MMORPG that allows mailing to alts, these additional characters will be used almost solely for storage space; as bank alts. It would quickly become the norm to have a full array of characters so that you can have a ton of bank alt space. The average player will fill out there character slots for this purpose. I mean, why not? It's a dollar more a month for more space than you can ever use. Best part is, many of these characters will remain unused and their inventories empty, because the other characters before it have yet to be filled up.
It's all just one giant mess that wastes a lot of space on the FFXIV database (all the unnecessary character data). And, for reasons truly known only to them, SE considers data storage to be this huge premium. They will simply never waste it like this.
Not to mention that it would kill their income from extra retainer services, but that's another matter entirely. <.<
Anyway, in nearly every other MMORPG I've played, I was an altaholic. I sympathize with the desire to use your main's fortunes to make the lives of your alts easier. Something should be done, but SE will never do it if it allows bank alts. Maybe it could be as simple as only allowing mailing Gil cross-character and not items?