Influenced unique items. What's the point?

Hi all. I finally got a stack of that divination card that gives you an influenced item and i received Meginord's Vise
This is a common unique, not a specific influenced unique. I already had a pair of those so i checked both and the "influenced" version doesn't have any additional mod. It's exactly the same except for the warlord icon and firy effect so what's the point? I can't even try to roll more affixes because it's a unique item.
I'm confused.

Well, shaped uniques can be used with eternity shroud and elder ones with replica eternity shroud.
But other than that they're mostly just collectors items.

It has no effect mostly.

But there are uniques which gave special boni if other items have a special influence.

Example:

https://pathofexile.fandom.com/wiki/Mark_of_the_Shaper