The first time I rode Carbon Canyon was in 1973 on a Schwinn Continental. Not much traffic then, and most roads in Berdoo county were rough and narrow, washouts and detours were commonplace. On riding this stretch today I would tend to agree that westbound on CC would be a fun downhill blast and going east uphill in traffic would invite real danger. Area from here to SA River burned in 2009 or so and is mainly known for mountain biking, centered on the trails in Chino Hills State Park.
Since my first ride there, the area has developed into suburbs and the area has lots of main arterial roads which are wide & in good condition. Many streets have dedicated bike lanes so there is no shortage of roadie routes. I don't live there but sometimes travel to the Jenson USA store in Corona. I like to get there from LA by Metrolink to Montclair, south on Central to the tangle of old dairy farm roads that eventually cross the Santa Ana River and a glimpse of almost wild riparian land. Then over a short ways to the West Corona Metrolink and the Jenson shop nearby at the 91 freeway (this leg is nearly all downhill). I then return either via train or down the S.A. canyon bike trail to Yorba Linda, then haul west on Imperial Hwy. to the Norwalk station of the Green Line. Ordinarily I only do this ride during the IE breathing season of Oct. thru May. Have fun.
Footnote: I notice there are group rides in Marin county which advertise a CHP escort on the narrow roads going to the coast. This is all done as an organized ride, at extra cost and by appointment etc., but soCal road riders are mostly left to the luck of the draw with regard to safety, as any review of PCH and related coastal area bike vs. car accidents will show.