For the most part uniques in PoE1 were just pre-enchanted items with perhaps some effect (taking up enchanting points), as you've pointed out. It could have made them more interesting had they one or more effects that didn't take up points, or completely unique and compelling effects, but that were not of a level to make them indispensable and therefore "must haves". Ideal unique items would all be interesting rather than all-powerful or, in PoE1's case, not different enough. One thing I found is that many of the effects already on uniques were ones that I could put on them, so the item's "special thing" was that it was gold colored and had a story to it. :/ An effect doesn't have to be very powerful to be very interesting, and therefore desirable. Think of this one, for example, and how much fun it would be use... "Character gains 10% of their endurance back each time one of their allies is knocked unconscious". Not too unbalancing, because you're sacrificing a lot to have it go off, but also think of how useful that could be in a tough boss fight... or what kind of silly battles could result from trying to min/max the usage. :D
I've had pretty good luck in RPGs I've run by making unique magic items have something different about them that makes the player emotionally bond with the item in some way. When they find a majority of magic items seem like they came out of a factory in China, the strange one suddenly becomes the one they want even if it's a bit less powerful, because it's different and therefore interesting. Giving such items little quirky things that don't mean much (if anything) in combat but make them stand out, can make the players unwilling to upgrade even when something much better (but ordinary) comes along. It's never been something I felt was forced in any way. It was just more enjoyable for people to have stories and a uniqueness to their characters.
That's what I'd like to see as well. The majority of items come from the drop system or quests (with vendors and "special circumstances" filling out the rest). You can then improve them, like with PoE1. While I love crafting in games in general, this kind of game isn't where I enjoy it as much. I'd prefer to have improvements that I can perform on an item to make it more customized and a little better than "stock", but I don't want to build items from scratch nor do I want the upgrades to be so mandatory that I'm compelled to do so on every item I get.