It should be more widely publicised that once men hit 40 ish their sperm quality starts to drop and there is an increased chance of having genetic issues with the growing embryo.
I have actually met a couple of men in late 40s who didn't get round to having babies and they regret that choice? not sure it was a choice they just didn't find a partner who was right for them, one had a job which was moving around a lot, not "travelling for work" actually living 9 months here, year here, etc so that is difficult enough to have any kind of relationship, well almost impossible as he explained, and the other, yeah I can kinda see why he wasn't chose as father material, little on the bitter side.
So I think men do regret some choices but it's hard to find ones that admit it.
And I do know that there were many men who didn't want to be older dads and wanted to settle down, have kids, build a career and life together, really nice men actually, but they wanted to do it first time with a first timer. These are more in number, from my very small sample, than ones who are in their 30s and get together with someone else with a child. I do know of a couple of those, one had a children far too young, but the mum was chill and took child back to her own country and he was the ultimate disney dad, travelling once a year, but kept up with communication etc, and another got together a bit later when he was too old to start up with babies but was fine with older kids and a more side role of not even being a step-dad more "mum's boyfriend" he was great with the kids but, happily, on the sidelines.
There are many exceptions to all sweeping generalisations with all humans, humans are so all incredibly different and fascinating.
But finding a 30s ish man, more left leaning, decent, good job/career, happy to take a role of step-dad and the co-parenting relationship, happy to date working around a 3 yr old, because school will start in a couple of years, not having that unbroken time of just being together, being spontaneous, that build up of free abandon sex all over the house at all times, I don't know, it's those beginning months that set the passion into a relationship and when you are both sleep deprived with an ill, grotty baby those earlier relationship memories, the fun bits basically, kind of keep you going and together.
So I don't think all men are players, probably more so on OLD, you know you sit swiping in the evening whilst sitting on the couch with not much else to do, little effort sex, I mean really little effort, they are not the men who are going to be happy putting in the huge effort you need for a relationship with a 3 yr old to consider, on the whole as a guess. And the men who do want to put in effort have an option to start a new family of their own, I think they are more likely to at least try that first.
So yeah in your 30s with a child I think is a difficult situation to find a decent partner, it's just an odd age for a lot of people, men and women, if they haven't already found someone or who already has children.