The music industry doesn't. If I were to ask you to name the city, place, or thing most associated with music, I'd get different answers.
Fashion, too. Sports. Wine. No Hollywood.
Silicon Valley is a good comparison, but when you think of software, it's shifted to the Bay Area and other places. It's not the same magnitude of definitive.
Hollywood is truly the dictionary definition, gold standard, 1:1 moniker.
Lots of the major production companies have actually moved out of Hollywood itself, and are scattered around Los Angeles (and the broader US).
Hollywood as a term has evolved a bit to just mean anything associated with the USA film industry, including Netflix, which itself has very little to do with traditional "Hollywood" beyond using some studios in California.
"Hollywood" is a gold standard, like "the Rolls Royce of X" is a phrase - it has captured the brand of movies, but it's current state today like you say is very similar to Silicon Valley - a name mostly (and it's used in a similar way, 'Silicon Valley North' for Canada, 'Silicon Alley' for New York, 'Silicon Beach' for Los Angeles, etc.).
Edit: Just checked and the production volume ratio between LA and New York is similar to the # of unicorns ratio between Silicon Valley and the next highest city. Really interesting comparison, as Silicon Valley has spread to the greater bay area and Hollywood film production has spread to the greater LA area as well.