I wouldn't share the photo's of my own children on Facebook. We lost a son to stillbirth and a daughter to prematurity.
We were not allowed to take photographs of our son, but if we had photographs of him I still wouldn't put them on Facebook.
When our daughter was born the hospital camera wasn't working. We'd gone in as an emergency and so didn't have our own camera. We have a couple of blurry pictures of her when she was alive and some more taken after she died, when DH went home and fetched our camera. He couldn't go before that, because they thought I was dying as well and he needed to be with me, and then when she was born we didn't want to miss a minute of her life by leaving her.
She looks beautiful in those photo's, like she's asleep, and if you weren't told she had died you wouldn't know it. I still wouldn't share her picture.
I wouldn't share the photo's because there are some sick and cruel people out there who would use them, either to claim as their own or to poke fun at the baby, and there are people who would complain as you are doing OP.
I think you are being unreasonable.
That man is posting in grief and gratitude. It may not be what you or I would choose to do, but it's obviously something he felt he needed to do.
Parents who lose a baby often want to talk about their child and share the few photo's they do have. It's their choice to do so and your choice to hide the photo if you don't want to look at it.
But don't come at them with "should do this" and "shouldn't do that" because it's hurtful and it's only your opinion. You might be posting things that they find equally upsetting.
I've seen far worse on Facebook. Most recently a friend shared a picture of a dog that someone had tricked into chasing a lit firework. As the dog picked it up, it exploded and in the photograph the dog is still alive, with the left side of it's mouth missing, covered in blood and looking very distressed and in a lot of pain. I think I'd describe the look on it's face as total misery. God knows what other injuries it had or if it survived. I have no idea because I hid the photo almost as soon as I saw it.
I understand why my friend shared the picture. He's very passionate about his own dogs, he hates any sort of cruelty. I agree with him. I hope whoever did that to the dog suffers long and hard, and I don't think I'd care if someone did the same thing to them as they did to that poor dog. But I couldn't look at that photo or read the article, I found it very distressing. I had to hide it.
I'd rather see the picture you described, of a baby that was loved and cared for in it's very short life, and a message of gratitude to the people who gave that family a little bit of time to say goodbye.