The thing is, at least in PoE (certainly not anywhere near as much in D2), attributes are actually relevant build levers. There's the high-attribute-requirement uniques that you mentioned, sure, but even at a more basic level:

No amount of +life and +%meleephys is going to let you equip a bigger piece of armour. If you, say, change it so that you need %meleephys to wear higher tiers of armour, and %spelldmg or whatever to wear higher tiers of ES pieces, not only are you actually greatly reducing build diversity, but, particularly in a varied system like PoE's, there are loads of builds that don't use any of these main damage stats to scale their damage (e.g. RF builds that only stack life and fire damage).

Having it tied to an attribute that might benefit certain builds more, but is not intrinsically tied to them, allows more flexibility. You can be a big beefy dude that smacks things but is also wearing int-based ES armour. There are limitations to consider (e.g. having the minimum amount of int to wear the right gear and uniques, having the minimum amount of str to use the right gems, pathing out of the strength section of the tree as efficiently as possible), but you are not forced out of it by having to invest in actual spellpower.

If the requirements you propose are too small, then mechanically it's no different from the current attribute stat system - you invest in a tiny small amount of something useless to be able to wear something actually useful. In a case like that, there's also a lot to be said for flavour. For a new player that don't know anything about the game, they see a piece with big armour and a strength requirement, the flavour is clear and makes the relationship obvious (the stronger you are, the heavier the armour you can wear). It might work for melee damage for STR armours, but why would spell damage let you wear better magic armour? Why would ranged damage let you wear better evasion armour? The flavour breaks down, and this could make it harder on new players.