I think that depends on the story of the particular item. The other major magic item my players' party possesses (well, possessed -- currently it's in the hoard of a green dragon upon whom they are plotting bloody revenge) is an ancient imperial scepter. To attune to it, they had to cobble together a jerry-rigged anointment ceremony and convince the item that one of them was the emperor. By the item's nature, it wouldn't work for just anyone.
Sure, but I think this is something of a tomayto-tomahto dispute. You speak of removing attunement but then adding this special linking mechanic, but that sounds to me the same as as giving out mostly items that don't use attunement and only a select few that do.
The scepter sounds fun, although I would argue that item user restrictions are a separate issue entirely, especially for intelligent or storied items. Your story even indicates that you didn't have the character simply spend a short rest with the item - as per attunement rules. So I would argue attunement wasn't necessary to have the exact same scenario play out as it did.
As for a 'linking' mechanic. It sounds like attunement but isn't really. The reason attunement exists is to place a limit of three attunable items on any given character and to slow down (through the required short rest) the switching of items. A pike that steals life and heals a character who has forged a connection to the item as opposed to any random person picking it up is a very specific thing, even if the attunement rule can generate a similar effect (and only due to your slight bending since a strict interpretation certainly would have prevented the barbarian from using it as a magical weapon at all). Only a very few of the items that are marked with attunement in the DMG could work thematically the way your pike did. It might even be worth creating a class of items that worked like that and you could even call it attunement, but the attunement rule is a larger and more prescriptive rule than that. Remove the three item limit and allow characters to use any item they have previously used reagrdless of attunement (no rest needed), and see how many items in the DMG still make any sense to have attunement as a property. Very few. The distinction may be a subtle one, but I think it is important.
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