The LA Riverin films from Wikipedia.
The Sepulveda Dam in films. (This is located in The Valley and well removed from the usual culvert section of the LA River used in films.)
You can dig around on IMDb for more, but stuff gets filed under “Sepulveda Basin” instead of “Dam”, etc.
A lot of natural rivers are dry or nearly dry at times. Parts of the Rio Grande, the last bit of the Colorado, etc.
What ever it is, it certainly isn’t a sewer ditch. I wouldn’t drink the water of course but it isn’t sewage. LA might be a figurative shithole but they don’t have open sewers there.
When I was quite young, we lived in Norwalk, CA. Friends and I used to ride our bikes along the San Gabriel river, which is all concrete like the LA river, but a bit southeast. It was very exciting when it would rain and the water would swell up out of the central channel for a couple of days.
I guess that doesn’t add too much to the discussion, except to say that the LA river isn’t unique.
Wasn’t it also where the giant ants lived in Them!? 
Who peed in your Cheerios?
“Why, yes, it was!” replied the poster formerly known as chopped liver.
From that photo on the Wiki page I’ve figured out the exact location of the drag race in Grease: that bridge in the background is the Fourth Street bridge in Boyle Heights, and the cars are underneath the Sixth Street bridge pointing north. See it here.
After further research, I can confirm that it is indeed the Los Angeles River.
I just saw John Carpenter’s 1981 Escape from New York, and the Dam and spillway are in several scenes as a U.S. Police Force helicopter base (it’s supposed to be on the same island as the Statue of Liberty). You can see it at the 0:27 mark here: - YouTube
Just saw a repeat episode of Conan where Conan leaves the studio and joins Archer in an animated chase scene.
That, of course, ends up in the LA River culvert.
'76 The Gumball Rally, the one with Michael Sarrazin, Gary Busey, Raul Julia, etc. I remember one scene where they’re assing around with their cars, Ferrari and a Cobra, and the action cuts right as one is definitely headed into a flooded portion.