Many airlines from South America and Central America that have flown to LAX throughout the years have done it via MEX without 5th freedom rights, Avianca was just the last one to do it. These days, it is just not viable to fly a tag along segment if it does not include proper 5th freedom rights.
Here is a list of the airlines that I've know that have flown the segment.
Aerolineas Argentinas: EZE-LIM-MEX-LAX
APSA: LIM-MEX-LAX and LIM-ACA-LAX (70s route)
Lan Chile: SCL-MEX-LAX (now SCL-LIM-LAX with 5th freedom)
LACSA: SJO-MEX-LAX and SJO-ACA-LAX (late 80s route)
In regards to Avianca, there is a large population of Colombians living in California, but like I've stated earlier many decide not to visit Colombia as often when compared to other Latin Americans in the area. Avianca also charged a very expensive fare for the ability to fly direct with them (approximately $1000.00 USD) when AA or UAL charged significantly less by flying thru their MIA hubs.
Pan Am - The World's Most Experienced Airline.