Using Intelligence for Attunement sense makes the most sense to me if you were to choose a stat to use, but if players are constantly dumping Int then they are valuing it the least for a reason. If Int checks came up more, that could encourage them to play more intelligent (not necessarily smarter) characters rather than maxing out Perception. Basing Attunements slots on Int causes it to be a (nearly-)required stat for all classes, especially for at higher levels. It's a bit forceful for my taste.
I love the atttunement system, and my players report loving it too.
Specifically because it enable me to hand out magical treasures whenever I feel like, and whatever magical items I feel like handing out, while minimizing the downsides of having done that because only 3 items or less with major impact on how the game plays can be employed by one character at any time rather than everything I hand out being able to be strapped on to somebody for benefits.
I will agree that there are probably some items which require attunement that don't strictly need to in order to remain well balanced - but I don't think I'd manage to agree with anyone which particular items those are, so I'm okay with leaving them all as-is. Better to be underwhelming, from a power relative to game point of view, than overwhelming.
We had an Iron Kingdoms themed 5e game where we built an Engineer class (parallel to rogue) which had an option in one of its archetypes to basically maintain one or more items that were "attuned" such that anyone could use them as though they were attuned.
I really like it. And as a 3.5 DM with item creation and +6 this and +6 that...nope, not again.
The only thing about a stat tie-in would be negative stats. If a fighter has an 8 Int, does that mean only 2 attuned items? It seems that would encourage meta-stating characters with the goal of maximizing eventual magic items (if any). I don't want to force a barbarian at level 1 to think "I'll just have to dump Cha and not use intimidate since I need Int for magic items"
I like it...but then again, I've used the "7 magic item on your person maximum" rule from the old Bard Games RPG The Arcanum. (yeah...7 magic items maximum on your character...otherwise they all stop working for you).
So far, nobody has ever gotten to the point where they had to decide to attune or not to an item due to having more than 3. Highest level campaign has been 6th level though...so there's that. In that campaign I also had a house rule that never came into play where a PC could get a "magic-item-set" that was created to be used together. Individually, the items were fairly minor, but once they were all together, their true power came to bare once a PC attuned to them. These items were all then "one item". A character could have the "Thasslean, Sword of the Waves [cutlass +1]", then get "Thassleans Guard [Shield +1], and finally acquire "Thassleans Helm [Helm of Comprehend Languages]". Once all three were attained, they became known as "Thassleans Trifecta", where they all together only counted as a SINGLE item for attunement. They also got other abilities (Sword of Speed, Shield or Reflection, Helm of Fish Command) added on to their original.
This made for one "super item", but it all would add to the uniqueness and history/background of the campaign world (not to mention player pride if he/she managed to get all the items in a 'set').
As a DM I have no problem allowing players to use however many magical items they've found. If I did I wouldn't have made those items available.... So I only apply attunement if I think that'll make an item more interesting. Likewise on ignoring it.
As a player? I don't care. It's rare that our games - of any edition - have had do many items where such a rule might even seem neccecary.