I do like the idea of treating a "set" of items as only taking one attunement slot. One friend of mine got a set of gear that altogether took something like 6 attunement slots, not even counting the gear he already had. (We were playing a Pathfinder module converted to 5E.) He ended up using only 2 or 3 items, and it just felt like a complete waste.
Even if it hadn't been an issue of system conversion problems, the idea of a set of magic items that are designed to work together on a common theme should be a cool and exciting thing to encounter, not a "Oops, you can't do that because 5E."