In Japan, some business do just that at the REQUEST of the government, because there is a vast underground economy that allows people to escape taxes. So the government gives businesses requiring non-cash payment tax breaks. 

It's also interesting that two of the biggest businesses trying to eliminate cash are stadiums (Crypto formerly Staples Center and Dodger Stadium). The reason for stadiums to eliminate cash payments is to reduce their cash-handling/transporting costs. Hiring security to pick-up and drop large amounts of cash is risky and expensive compared to non-cash arrangements. 

Both stadiums are likely incurring major costs for cash-handling.

City government officials say that they are concerned about people who rely on cash-only purchasing (people who avoid having back accounts) should not be "excluded" from being able to, "enjoy the city". 

It may also be that organized crime has some influence over L.A. city government policy. Remember this is the city whose mayor made a public statement to criminals completing their prison terms, in which he said (verbatim), "...thank you for your service", as if he were thanking soldiers who served in the military!!! Criminals tend to dislike and have much discomfort with an economy that is non-cash. 

Sure, there are libertarian arguments against banning cash purchasing, but there are so many businesses which can't afford to ban cash, I really don't understand the city's policy unless they are trying to help out the Mafia to avoid paying taxes or being tracked by law enforcement by their purchases.