Unpopular opinion: I get that V had post partum depression, but I feel like writers choose the wrong parent to not connect with the twins. Yes, everyone loves daddy Kev, but you can see how maternal V was. They've established that they've known the Gallaghers since Carl was in diapers which explains why the kids were so comfortable going to V for help and using their stuff, Kev would get upset so it was V who offered. I can see her taking a teenage Fi under her wing to help raise her siblings.
This is an interesting thing to think about. I would like to talk about it a little further. I think that V being a maternal figure is something that has been apart of her since the first episode. Like you said she has been around the Gallagher’s for most of their lives, she took care of them when her husband didn’t want her to. Just like many maternal women do. Post Partum depression doesn’t come to only those who aren’t maternal. It can happen to any woman, especially those who are great mothers.
When I was in a psychiatric hospital there were several mothers in the facility for the very same thing, they are just women who want to love and connect with their children. They want that more than anything but for whatever reason they don’t have that, and it makes them feel like terrible people. Kevin not connecting with his children would not represent those mothers, or the real struggles that shameless likes to portray.
Because of V’s maternal instinct, her having these struggles is realistic. It shows that there is no way of preventing this happening. If Kev didn’t connect with his children, I don’t think it would have had the same impact on their family or for the audience. A man not connecting with or being able to be a father is not something that happened because of his hormones or the chemicals inside of his body like it does to a woman who gave birth to them. It’s a different type of PPD and possibly wouldn’t have come across on screen as well. If V was the one upset with him for not connecting with or ‘loving’ his kids the 'right way’ then he could possibly have looked like an asshole deadbeat like many other fathers in their neighbourhood would have been. It would have probably damaged his loveable character and caused drama in the relationship in a different way.
I do see where you are coming from. Kev being so excited to have children and then it not turning out the way he thought would have been interesting also. But I think they took a great opportunity to represent another important issue women face, and they did a pretty good job at showing it and how it affects a husband so passionate like Kev.
This article is interesting and I recommend reading it.