There are certainly positives to being a single, part-time parent. Although I consider myself a full-time dad, having my kids with me for one week, and then away the next week, means that I am not parenting all the time. And while I miss them terribly when they are not with me, it does open up opportunities for other things.
The things I am referring to are extended periods of time to do what I want to do, hang out with the people I want to hang out with, and generally use my time on understanding and expressing myself however I feel without anybody commenting or influencing me.
I see this as a contrast to when I was married and living with my wife and kids all the time. It was as if we felt we had to do everything together. I can't really remember doing many things by myself during that period, apart from going to work. I don't think I gave my wife the freedom to explore and express herself; I am not sure I could have handled it. And I did not take that on for myself either.
Now that I have been forced into it, I can see that I am able to handle being a solo parent for extended periods of time. It is difficult for sure, but it is possible.
The question that comes to my mind then, is whether this is possible for people who are still in a relationship? Can they give the other parent extended periods of time to explore projects, hang out with friends, go on holidays, while they look after the kids by themselves?
I think it is possible, and could even be better. My retrospective guess at why this is not commonly practised is that there is a fear of losing the other person; that in giving them room and space to be explore themselves, it could mean the end of the relationship. They might discover they want even more freedom, or we might find out we don't like who they truely are.
In having a week to myself every second week I have found great freedom in following my curiosities without constraint. I can imagine that this would be even more exciting and fulfilling (and risky and scary?) if conducted within a relationship.