I was very good at most subjects in school, not because I had any particular aptitude in them, but because normally on the first day of school they'd hand out schoolbooks, and I'd read them.
Usually with these types of structures you'd have not because/ but because with the latter clarifying why in once single sentence.
With this example it ends with - hand out schoolbooks, and then adds that the writer had read them.
Is this ok grammatically?
I'd have written it: they'd hand out schoolbooks which I'd already read.