I find this trope to be self-serving in the extreme, and deeply ignorant of the practical realities of education, poverty, and parenting.
I remember reading during the Chicago teachers' strike that with public schools closed, many poor kids would not eat lunch, or possibly at all. That is messed up in a way that transcends any thoughts we might have about the best way to educate.
Yes, it is a messed up situation all around, and the roots of the problem lie far outside the realm of education; yet no teacher can be successful at their goal of educating children, now matter how they go about it, without dealing with those problems.
I grew up in somewhat unfavourable circumstances myself and did not do well at school. Then I taught myself a profession using the "problem first thinking" approach. It has yielded great results. I wouldn't have wanted the teachers to account for my disadvantages by giving me a crippled education. I do, however, wish that there was some organisation which would have addressed the problems I was having.
Like I said, I agree that the issue must be tackled - just not by teachers. Why should someone who is trying to teach calculus waste their time on adressing emotional needs? A psychologist doesn't concern himself with teaching IT skills, after all. I would agree that it's the teacher's job to raise a red flag if they notice something odd, but let someone trained in the field deal with resolving it. Most people barely master one field, let alone two.
The problems they inherit from poverty or poor family life are not resolvable through education in the first place. That is a separate issue which requires just as much attention, but it's not a teacher's job to do so.
Giving those children a route where they can skip learning how to think and instead memorise everything is putting a bandage on the wound, not healing the illness.
Moreover, when we talk of different learning styles, it does not mean that one human is robotic in their thinking while another is not. Learning styles are about how to communicate information - i.e. through visual, auditory or kinesthetic means. There is not one person who would not benefit from learning how to think for themself, just as all people benefit from learning how to use their emotion and intuition to inspire creativity.