At primary level perhaps this does not matter so much because it is believed that children at this level are not able to master the material at such complex levels as, say, secondary children are

Well this is where school is wrong for so many children, children like mine are very able to but they are not able to write it down till secondary level, or not sufficiently to demonstrate the sophistication of their understanding. They have problems transposing numbers so make mistakes in simple maths but later go on to understand complex proofs and logic with relative ease. Primary school especially is abusive as performance is all that matters, performance and stats. School tells these children that they are unintelligent and a failure and how many never learn different, I had no idea of how very wrong they were about me until well into my 50s. Home ed lets the child learn and teach through conversation, hard to imagine how school could match it. Perhaps if it became a resource to help children answer their many questions rather that shut up sit down keep still stop talking. Due to my own dire and abusive education where I was blamed and shamed for having a different brain not a plodding sequential one but a leaps and spurts and make odd connections one I have protected my children from the damage schools do to people like us. We are the wrong shape for mass teaching, but I have learnt a lot about learning and child psychology and development in the process. Good luck with your Phd, it would be wonderful if a change that protected neurodiverse kids from plodding repetitive curricula and being profoundly misunderstood could could be instigated but you must know that government usually go in exactly the opposite direction of what quality research suggests would be efficacious.

Thing is children who are home educated can play through the primary years and pick up everything that is taught so laboriously to the children trapped in the classroom for so many hours, so many years, as a bi product of play and curiosity.