I think the starting point of this is the understanding that women who make these decisions are not coming from the same starting point as women who don't. It's not a level playing field decision.
I'm going to try and say this as sensitively as I can because I don't actually want to upset anyone and I will caveat it by saying I grew up in abuse and had my first child within an abusive relationship so I don't think I'm pissing in the wind with this and I can see how it could have easily been me too. But it is also just my opinion and I'm not staring it as fact.
IME, many women who have three or more fathers to their children have grown up or lived within or been exposed to abuse or dysfunction. So, IMO, the decision is often rooted in trauma/a trauma response.
When people grow up in abuse or have lived with abuse, one of the fears (in my experience) is being seen by everyone as the person your abuser sees you as - weak, incapable, incompetent, worthless, undeserving, unseen and unheard, ugly, unlovable - whatever their focus was. You are mocked, 'invalidated' (God, hate that word!) and feel 'less than'.
Your drive is to correct that; to prove to yourself and everyone else that you are just as good as them. (Or, conversely, they become core beliefs and you accept that you are all of those things.)
Eg some people correct it by going to university (thats what i did. If i was going to be judged for being a 'young' single (not by choice) parent - and I was - I was going to be one with a degree); some correct it by focusing on their career and earning a high income to be completely self sufficient (and a lot of the high income/career threads show this and it's what my brother did); some correct it by focusing on building a small, close, supportive, loving family and ensuring their children never experience what they did (again, my brother and i did this). Those are all healthy responses (I think). And there are probably many more I haven't thought of.
Some decide not to have children because they're worried about their skillset as parents and the cycle repeating (I've read that on here too). I think that's sad but understandable.
Some people chase approval, love and affection. But are not sure what it looks like. They haven't healed from the past and so are destined to repeat their mistakes. Again, that is evident from relationship posts on MN in general.
Being single feels like you are those things your abuser said; having a child feels like he will step up and raise his game (and how many threads are there along those lines!); being a family feels like you can do something right.
Some women, as has already been said, feel that they are still judged and invalidated (for relationship failures) and so having a child within a relationship makes it more real. This is the relationship that is going to last. This is the decent man they were worthy of the whole time. This is the man who loves them. But they are unable to see certain red flags that would suggest to others he isn't the decent man they wish him to be. So those men don't make good partners, good dads or stick around. But they still hope that this is the relationship that will make them seem a real person, one who is worthy of love and a baby proves it. In their eyes. And sometimes they stay in those shitty relationships for fear of being judged for that too.
Some women, who've left abusive relationships, want the experience of 'normality'. The experience of pregnancy and birth and the early days and child rearing and family life with someone who is supportive and present. And they hope that this man will be the one to provide it. Sometimes this is the third man and so it goes no further. Some times it's never the right man and so the cycle continues. Some women crave it but decide not to have any more because they don't want 3+ children by 3+ fathers for a variety of reasons.
Some women crave the attention and validation of being 'mum' (because its lacking in other relationships in their lives) and so continue to have babies for that reason. The snuggliness of baby cuddles etc and crave that when the child starts to grow and so have more. When the previous partner hasn't stuck around, this is only going to happen with the next new relationship.
Some feel entitled/a desire to have that positive experience - why shouldn't they have that experience that we read about in magazines of a loving, supportive partner? And why shouldn't they? Some women (eg on this thread) feel unfairly judged and will explain - but I was in an abusive relationship etc. Some decide to not risk it happening again and decide no more children.
These are largely trauma based, emotional responses and not logical or 'intelligent' ones. Not to say they're 'thick' or 'stupid' but they are heart decisions and not head ones. They are not rooted in practical decisions such as financial stability, childhood experiences, child/parent relationships etc but in personal desire and want.
As I've said, I chose badly (although I didn't realise it at the time) twice. OK, my exh has been a reasonably good (not brilliant) dad to his children and he took his stepdad commitment to 'our' eldest seriously. For which I am thankful and respect him. But he was not a good dad when we were together and he wasn't a good partner to me. It would have been quite easy for me to become one of these multiple children by multiple men women. But I made different choices because I believed they were the right ones for me and my children.
So the need to 'seal the deal' is not one I made. But I do understand the basis of the drive to do so.
I understand the concerns for the children and agree. Like I said, I worked in CP and now work in education. I've seen lots of dysfunctional relationships of all dynamics professionally and I'm mindful of how they arise. I also see the impact on the children and it's not a posiitve one.
This post is already long enough and I've only really scratched the surface of how/why I think it happens but I think that if you don't understand it at all, be thankful for that.