The reason we don't have a tackle box is actually quite simple: Yoshi P has said that when they add more inventory slots it is far preferable to add slots you can use for anything, rather than adding slots you can only use for one thing.
That way the people that want the space to store tackles and lures can use it for that.
The people that want a "crafters bag" can use the space for mats.
People that want a "dye box" can use the space to collect their dye.
Etc.
He has actually been very clear on this. And this is why we got the chocobo saddle bag.
He has said we should never expect to get new inventory slots dedicated to specific things (like a tackle box) when we could get... just... more inventory.
