"education is only a small part of a child's life"
I think it depends if YOU choose to make it a small or large part of his life.
When DS was in year 2, and I did not work full time - so in your situation - he walked to school, which took 5 minutes. He was in school from 8.45 until 3.10 each day, and had essentially no homework other than reading, which we would have done anyway.
He woke up at 6 am every day, and went up to bed at 7, lights off at 8.
All other activities - swimming, Scouting, football, playing in the park every day after school etc - were all out of school, predominantly with one of his parents around, 'mediating / interpreting' that experience to some degree for him (he still wasn't fully better at that point). However they were important 'socially' for him, as he interacted best with other children when they were 'doing the same thing as him' so there was something obvious to talk about / do.
So from each day, school was 6.5 hours, out of an 11 -12 hour day, and didn't take up any of any weekend. So in those circumstances, yes, school was, although important, not the 'consuming part of every day'.
However, if you make all of every day about school - get up early to get to school, spend a long time getting there, be at school, spend a long time getting home, do lots of homework, have no out-of-school clubs, even have Saturday morning school - then yes, school DOES have a much larger influence on the child's day to day life and experience. And I can see that if you choose to make school 'the only thing that happens every day', then you are making it ultra-important. That seems to me to be a little 'cart before the horse' - you regard it as important, so you make it ULTRA important by filling every day with it...