Sure, if you can bother with having two (or more) different sets of stats you switch between.
Absolutely.
When I shot from the hip and suggested 10 attunement points (where a major attunement item now requires 3 of those points) my focus was squarely on a single set of stats - that the player makes a choice which items to attune to, and then sticks to that choice (for convenience or whatever reason).
You could even say you get 1 attunement point per character level, in order for an item that is overpowering at low level can be reasonably be attuned to together with other items by a high level character.
For instance, if one particularly powerful item cost, say, 7 attunement points that would mean
- that a level 1-6 character simply can't use that item
- a level 7-9 character can only attune to that item but almost nothing else
- a level 20 character can easily attune to both this item and perhaps two others no problem