I think "mental load" is a parenting thing before it's a female thing. The dads I know all look as stressed and tired as the mums. I was told on another thread that the "mental load" didn't apply to me as a child-free woman, which is correct to be honest, and sort of the point.
As with everything else to do with how hard parenting is, part of me thinks, well, you signed up for it all. There was always the option NOT to have a mental load involving endless school letters and buying kids' shoes. (As an aside how often do you even have to buy school uniforms and trainers etc? Surely that's not exactly an everyday task?)
As for the fact that all of your husbands don't pull their weight... it's just not reflected in my social circle. Like I said, most dads I know look knackered. Very few of my friends who are mums have complained about a husband who doesn't do his fair share. In my relationship, DP is the house-proud neat freak and I'm probably the one who doesn't pull my weight domestically, if I'm being honest.
Finding a partner who will pull his weight and then ensuring that happens is something you have agency over. At every stage.
I also suspect a lot of women take on an entirely unnecessary "mental load" - there are always a few who say that remembering their in-laws presents (and cards?!) is part of the mental load. I have no sympathy at all with that. Just don't do it.