Fairly often, actually.
During normal play, I gather materials such as Runes, gems, jewels, Rares, Shrines, etc. to keep on-hand so I have them right when I need them instead of breaking the flow of play to hunt for them. Later, when 3/5 of the inventory is filled with just Charms (to say nothing of Cycles), it's easy to get overburdened when farming multiple locations in a single game.
But even if others don't play the way I do, Inventory tabs would still be more convenient than Stash tabs for the other reasons I mentioned. Especially if some Ubers are going to be restriced in various ways (timers, no TPs, etc.).