In a perfect world, where the parent leaving took equal responsibility for their children, put them first, paid what they should and all the rest, I'd agree with you OP.
In reality, that rarely seems to be the case. As PP have said, it's usually the father leaving, he might have the best intentions to begin with but then a new girlfriend or hobby comes on the scene and the resident parent is left doing the donkey work while the Disney dad takes the kids out and stuffs them with ice cream EOW.
I'm also at a stage where I see many of my friends divorcing and embarking on blended families, and although they say things like "the kids love it, they get on so well", nine times out of ten I'm not sure that's the truth. Of course it can be successful, but it takes a lot of time and effort, level headed common sense, detachment and fairness on the part of the couple, and who has that when they are in the throes of a new love, wrangling a squad of children half of whom aren't your own, plus dealing with the various ex partners? Hard, hard work.
I'm not advocating staying in miserable, abusive marriages of course. Divorce isn't the problem- it's how we deal with the aftermath, and specifically it's how society lets men away with blue murder. Throw your kid an ice cream and stick them in front of the telly EOW and you're an amazing dad. Meanwhile the single mum slogging her guts out is fair game for criticism. It's not right. I'm a teacher, and I often find that the children who come to school with no books or equipment, homework not done, uniform a state, a bit smelly, low level behaviour issues - are the ones who've just been to dad's for the weekend, and then they tell you that he left them to play xbox while he fucked off with a new gf. This is all purely anecdotal, but we see it time and time again, and for some reason it's more obviously boys. I have so much sympathy for their mums - we ring the parents, dad doesn't answer, mum does, mum sends in the new book/blazer or whatever in the next few days, child seems happier,work and behaviour improves gradually over the next few weeks- then dad wanders back into the picture and it's back to square one. It's not fair and it's not good enough but what on earth can be done? Nothing will change until it becomes difficult for men to neglect their responsibilities. Thousands of men don't pay child support and not a word is said, it's easy for NRP to get away with doing a shit job of parenting while people clap them on the back for still actually seeing their child.
OP, in your cousin's case - eighteen months ago they were clearly in love and thinking of the future because she became pregnant - now eighteen months on and he's left?