> If it's on a street... how is wealth being built?
It's tax revenue, aka wealth, for the city. That counts for homes and businesses.
> And how is it not connecting productive places (your home to your office)?
The main purpose of a street is access to the productive places which is different from a road. The main purpose of a road is connecting two areas with productive places, usually attached to streets. A street has businesses or homes lining it, a road should not.
> but separating their usage actually leads to more problems than solutions.
No it doesn't. You want transportation to be fast and efficient and you want streets to be safe and accessible.
> Roads and streets are synonyms.
No, they're similar but are designed for different things. My smartphone and my laptop are both computers but we call them different things because their uses are different.