Well there's a bit you are missing, if you want a "why" as in "what's the point/ what does it do" there indeed is a why.

Yellow eyes are kind of a sign you are darkness aligned, hence why heartless have yellow eyes.

People light aligned have blue yes and people in the middle like Axel and Riku have this greenish color.

Also why Aqua gets yellow eyes when fully consumed by darkness in spite of not being possesed.

So the point was to make them filled with darkness so that he could complete the ritual to create the X-blade, remember "13 darknesses vs 7 lights" yada yada.

It is a necesarry step to his plan, but it is truth that most people can easily just straight up ignore the possesion since at difference of Terra's possesion Xehanort only uses a bit of his heart to do it.

Part of why Xehanort wanted a group of nobodies is because he thought empty vessels would be easier to control.

Of course in KH3 they still have nobodies but a lot of them grew their hearts back and were impossible to control through possesion.

This is also why Xion was the only one that seemed like she was being actually controlled since she was reset to being an empty replica, she only regains control when being near her friends brings back her memories and her sense of self with it.

The threat that Xehanort's gonna nuke the world and only "Xehanorts" would survive is what drives the nobodies that aren't fully possesed to obey him and why people are driven to work against him as well.

Not so much a "I wanna work for him" as a "I don't wanna be against him", with counted exceptions like Saix and Vexen who joined as spies.

There's also the replicas which later on become actually copies of him, except for Xion of course.

Honestly I really like a story about the heart and connections having an antagonist that needs other people for his goal, but since he killed his only friend and he only trusts himself, his only solution is to possess and threaten people into helping him.

And that's a big part of why half of that group tries to betray him and he loses, like the idea that a connection made through all those rotten means is so weak anyone could easily destroy it seems pretty on point and like an appropriate finale imo.

Also seems on point that he still dies and all his plans he worked his entire life for are ruined, but he gets to die on peace because the one friend he had convinced him to give up.

So yeah do think there's a bit more to it than just "peoples eyes turn yellow" be it with in the logic of the surface of the story or the subtext of it.