Hmmmm...then I think we have a good candidate for an errata document, either re-classifying some items, or re-writing that sentence. I vote for the latter.
Don't the permanent items require attunement and thus hit the 3 item limit? Meanwhile the consumables don't count to that limit, and can always be used.
DMG. p. 135 "Rarity provides a rough measure of an item's power relative to other magic items."
I don't think there's anything wrong with the term "rarity" being used in this manner. +3 swords are significantly more costly and difficult to create than +1 swords, so there are far fewer of them in the world. They're both more powerful and more scarce.
The fundamental idea is borked.Just because something is flawed in its implementation doesn't mean I can't like the general idea behind it.

(Dungeons & Dragons)
Rulebook featuring "high magic" options, including a host of new spells.