While I certainly agree that elements of the school day certainly can--and should--be personalized, completely doing so would take away from a huge piece of education: the participation in a democratic society.
The graphic above is one I used as a visual representation of an Inquiry Project not fully nurtured. Students came in to my class, spent time researching their individual questions... but our classroom felt very lifeless in those weeks. Though students made wonderful discoveries, they were disconnected from each other. This seemed like such a shame... Here we were, together--yet completely separate. Shouldn't I be working with these students to look at our crazy-different selves and say, Can you imagine the amazing things we could we create together?