I'm not thinking day to day storage, but would be nice to just huck the Arbor Trolley, hand truck, rakes, etc.
I don't connect all my big rigging, but it stays in a big lineman bag. All smaller rigging (biners, pulleys, cordage, etc) should be clipped together, and bagged or in a rubbermaid container. It takes much more time to make $300 in profit for some lost gear, than to compartmentalize it (have a compartment where you can know where it goes and where it will be, and to some degree makes it easier to visually check.
Also, being able to lock up a mini or log arch or the like that don't fit elsewhere, would be nice.
Problem with a top door is that it would block the truck signs if it were to fold and pin open like the lower door.
I'd second that notion that get more boxes than you think you can use.
Add in custom shelving in a tall open box, or build a little bed slide if helpful on a through-box, splitting the box into an upper and lower.