I don't think it is unique to CA, I've never heard it any other way in other parts of the southwest.
Back in IL nobody did this, at least not when I lived there over a decade ago.
A notable exception is Lake Shore Drive (US Highway 41) which everyone just calls “Lakeshore” in conversation with no article.
The economy of two syllables instead of three wins I guess.
I grew up out in the west suburbs, everyone just said "88" "53" "59" "355" "i80" etc.