What's your stance on staying FB friends with your ex if you never see them or talk to them in real life?

My fiance and I have a mini-argument every few months because he will not block/unfriend his ex from his FB. Normally, I wouldn't mind, but FB hates me and always puts this girl's face at the top of his friends list, so I see it every time I'm on his page (why taunt me, FB algorithm?). She also posts about twice a year: "Happy birthday, nickname-I-called-you-when-we-were-together" or "Aw, I miss your mom!" on a picture of his mother.

The girl lives hours away, is married with kids, my fiance hasn't talked to her directly since they broke up about 8 years ago, and we are blissful in a great relationshgip so it's not like I'm actually jealous of her.

She annoys me, though, and my argument is that he doesn't really get anything from keeping her on his list, so if it annoys me, why not just delete her? His argument is that his other friends will notice that he unfriended her, assume I made him do it, and it will make us both look bad.

I'd happily block/delete my exes if he asked, by the way. I never talk to them, so meh, no big loss.

Thoughts?

PS- Yes I did use my first GT post to show what a insecure, jealous, controlling girlfriend I am every now and then.