> The yellow lines are the stations built along freeways.

Per the legend, that's "existing right-of-ways" which include freeways and existing railways.

> Only the tiny non-purple, non-yellow fragments were built where the actual demand is.

Well, except for much of the East Bay (certainly the two northern lines, which I'm most familiar with), where the freeways BART follows (including the tunnels that follow them) also run right through the heart of the main cities.

Just because they had existing right of way of leverage doesn't mean that it wasn't where the actual demand is.