I think people have an image of those who abuse children as being evil, wicked, not loving their children etc. And there are definitely parents like this - I think this type has less to do with poverty and yes may be more hidden / downplayed / ignored in more privileged / wealthy families (maybe even making it worse in some contexts because it can be concealed?).
However I think there is a larger proportion of abusers, who could be better described as incapable or deficient or simply unable to cope with the life they are living than they are intentionally wicked, if that makes sense. And this group can also be either poor or wealthy, but I think this scenario is more likely to be linked to, or worsened in impoverished situations. Both because poverty is hard, a massive thing in and of itself to cope with which may reduce parenting capacity in those with lower resilience. And because having lower personal resources or problems with trauma, mental health or addiction is more likely to lead to poverty (with the exception of eg the landed gentry / celebrities etc but overall these are a small minority of the population).
It is easier to break generational trauma (which is a major source of child abuse) the more resources you have eg money for therapy, time / space from the pressures of daily life to reflect and decompress, adequate sleep, good diet, exercise etc that is going to make it easier to behave as your best self. These things are harder to accomplish if you are facing poverty. Poverty is a disadvantage. It's going to make everything harder, including being a good parent, from whatever your baseline is. Obviously some parents are going to be excellent no matter how poor they are, and some parents are going to be dreadful no matter how wealthy they are, but for parents for whom it does make a difference, being poor will almost always be a negative factor. It's similar to how poverty might make it harder to perform well at work and becomes a "trap" for various reasons.
And being traumatised by abuse as a child is going to affect your life chances negatively. Obviously, many people with this type of background will become successful / wealthy but on average those who are abused in childhood will suffer negative health and social consequences throughout adulthood that may, again on average, have a detrimental effect on earning capacity. And unfortunately being traumatised by abuse is a risk factor for perpetuating abuse on one's own children.
Obviously, generational trauma also frequently occurs in wealthy families but as aforementioned the adults emerging from these families may have more resources available to them to overcome that trauma and break the cycle.
Poverty itself is the villain. Society has a responsibility to prevent children from growing up in poverty, and to help all, but especially disadvantaged, parents facing trauma, MH problems and addiction to overcome these difficulties so that they can be the best versions of themselves for their children. But at the moment society is failing in that goal and I believe there are real consequences for children (eg increased abuse) that result from this.
I also find it very believable that lower income/class parents are subject to discrimination/ increased scrutiny compared to wealthier parents. That can be true at the same time as poverty being an important factor linked to child abuse.