The point is the headspace given to manouvering and resentment.
Of course fathers are perfectly capable of buying and washing clothes. Of course most of them do. But when you find you are stuck with a dad who doesn't seem to want to do this, what's the plan?
Make good your other parent's deficit by ensuring your children remain decently clothed, or embark on a war that you can never win, and let your children see how their parents can't let a damn thing go in the fight for victory, because both their parents cherish the fight with the other parent over their child's peace of mind?
Kids know what their parents are doing. They suffer it, with far greater and lasting damage than a mum does having to do a bit of extra laundry (We're not taking it to the river and beating it with rocks, FFS!) In 20 years of practice, I've seen disputes about this trivial shit (which is nothing to do with the kids and everything to do with the parent's rage) spiral to the extent that the kids were required to strip to their pants before entering father's home, and consequently, then required to do the same on return to mum. But it doesn't take that level of dysfunction to tell the kids what is really going on : hating Dad is more important than loving them.
I know It's hard, I'm not just a family lawyer, I am also a nearly 12 years separated mother, with all those years of incompetence, selfish thoughtlessness and continued bullying under my belt. But ultimately, my job and my life have taught me something I think is vital. Look at your child. Stop looking at your ex, and yourself, and look at your child. What matters to them? Because nothing else matters in this setup. Does it?