In the Los Angeles market, Spectrum already a local news channel, but it only serves the Antelope Valley portion of Los Angeles County. L.A. itself is already a news-heavy TV market, especially given the fact there's a newscast almost literally every hour from 4am to 11:35pm every weekday (and in various languages at that), and with that there's never been the big push to launch a cable news channel here locally.
The closing thing we have had was the Orange County Newschannel in the 1990s/early 2000s...they had backing of the Orange County Register and Century Communications (which later became part of Adelphia), but it was only limited to Orange County cable subscribers, and maybe a few areas along the L.A./Orange counties border.