The parts were reused but they rebuilt the whole thing from the ground up, everytime. Reusability means something like a plane: refuel + safety checks and you’re good to go again
Reflying the booster cases doesn't change the fact that an essentially new solid booster has to be manufactured.
In fact it didn't even financially make sense to reuse the boosters, so it was actually worse then not being reusable at all.
As with everything with Shuttle, it all sounds cool when you imagine it, but then if you look at the actual program its basically a 40 shit-show that started very badly and basically never got better. In actual fact, it failed completely as an industrial program for the US.