The plan of storing only items you're going to want soon and can't easily re-obtain, while selling off everything else, would indeed cut down on how much storage space you need by a great deal.

Unfortunately, it also means every time you get an item, you need to research the item's value. Can it be gathered? Can it be purchased? Where? For how much? What recipes need it directly? What recipes need it indirectly for one of their intermediate ingredients? Am I going to want any of those items any time soon? Do any leves or GC supply missions ask for any of those items? ...

Sure, if you're willing to spend twice as much time on inventory management as you spend actually playing the game, you could check all that and pare down your inventory to just the most useful items. But for people who don't want to devote the majority of their game to inventory, it has to be a much shorter set of questions, something like:
Is it a crafting ingredient? Yes. Do you do any crafting? Yes. --> Keep.
And that makes you run out of space fast.