There are 2 heavy rail system in LA, the Red and Purple line compared to 5 BART lines. There are 8 Metrolink lines in LA compared to just one CalTrain line by the Bay. And SF has 7 Muni light rail lines compared to 4 in LA.
So it isn't true that SF just has one BART system. You might be surprised how many rail miles and train stations LA has compared to SF.
LA miles, stations, and ridership by train type:
Light Rail = 70 miles, 69 stations, 357,000 total
Heavy Rail = 23 miles, 22 stations, (")
Commuter Rail = 388 miles, 55 stations, 42,000
Total = 481 miles, 146 stations, 399,000
SF miles, stations, and ridership by train type:
Light Rail = 34 miles, 33 stations, 87 additional stops, 150,000
Heavy Rail = 104 miles, 44 stations, 374,000
Commuter Rail = 77 miles, 32 stations, 47,000
Total = 215 miles, 109 stations, 571,000
Believe it or not, Southern California has more rail miles and train stations than Northern California. Maybe that's the result of not building as much more expensive Heavy Rail. But Northern California has more weekday riders today - it'll be interesting to see how LA ridership grows as they expand all their rail systems.
As for why they didn't copy BART as much; they don't have SF Bay to run tracks under.