It is hard when our parents and other people we leaned on growing up ignore difficult issues and pretend they don't exist. I'm not sure one's family history automatically fits into that even if the reasons given are around not wanting to rock the boat. We can not want to look into things without actually ignoring or pretending it isn't there, it can just not have the same draw for them as it does for you.
cover for people's psychological maladaptations rather than challenge and improve them
You cannot force someone else to improve their maladaptive behaviours. Unpicking well embedded ones takes a lot of patience and on-going consideration & care, not something you can just challenge someone on.
I mean, if they turned around and said your "personal project" might be a maladaptation to seek out more recognition of the truth than you grew up with and such a drive led you doing something rather thoughtless and risky, I doubt such a challenge would neither do much good for the relationship nor have you seeking another path for dealing with that pain. I know if someone had told me that digging through court records wouldn't give me what I was looking for, that as nice as that formal recognition by seeing that charges would be, that I'd end up with more questions than answers and just a feeling of being failed, I'd probably have told them to feck off. If my parents had tried to suggest that, oh, I'd have had more than a few choice words.
This is the basic idea behind psychotherapy - bringing uncomfortable truths into the light for better mental health.
There are dozens of therapeutic models. Don't use the 'basic' or most well-known one for all situations. That way lies to harm.
It's widely acknowledged in many trauma-informed therapy models that bringing uncomfortable truths to light doesn't always help, it can re-traumatize people and people can pick at that scab over and over. This can become its own maladaptation, even a method of unintended self harm disguised as doing good. Bringing up pain for recognition can give quite the dopamine hit - been there, done that - but it doesn't end up helping our thinking and emotions in the long-term and often leads people to bringing it up more just so they can get that recognition buzz all over again when we feel we didn't get it properly when it happened. I fall into that trap a little too often.
I get the draw - I grew up with a very patchy understanding of my background, I grew up with a lot of rumours, many of which I'll never know the answers to, not confidently. I was in my thirties before I felt sure that my father is actually my father, I'm the spitting image but there were a lot of 'milkman/delivery man' jokes growing up that those doubts lingered.
I'm far less sure on my paternal grandfather, but I've chosen to let that lie - what benefit would it be to anyone else if I dug into the rumours that my grandparents married because my grandmother was pregnant by someone else, that that's the reason my father looks so different and is the only one who didn't follow in my grandfather's footsteps? Honestly, having been the target of malicious lies around my paternity in part because I'm darker and different to my siblings, I can give my grandparents the benefit of the doubt even though I'll never be sure.
DNA tests can be interesting, but there are just as many stories of them causing pain as stories of them causing joy. Just because there was pain for "the truth" doesn't actually mean the pain was worthwhile - sometimes it is, but being the truth doesn't always give pain meaning. It's more complicated than that and with this sort of thing, it's hard to know which you'll end up with. It's a risk, and not everyone wants to take it. There is a difference between hiding from truths we know are there & festering and just choosing to let sleeping dogs lie.