"We as a society" didn't really do this. The banks, however, really like this, because it solidifies their economic position. Imagine how much more money they'd make if everyone is required by law to make all their transactions through them.
Who do you think is trying to convince people that this is the right way to do things? How long have we associated "anonymous transactions" with terrorism etc.?
Only recently, we've developed the idea that something must be wrong with you if you use cash. $100 doesn't even afford a meal for two at a nice restaurant and people look at you like you're a drug dealer if you carry a $100 bill.
Yes we did, in reaction to the fear of organized crime, especially in urban areas. Anti-money laundering laws were the direct result of efforts to combat organized crime (the Bank Secrecy Act, the Organized Crime Control Act, and RICO were passed in the same year, 1970).
And you know what? It was extremely effective--so effective that we've got a generation of people who don't even remember what a huge problem it used to be.
Yes, we most certainly did. Start with the Bank Secrecy Act which was enacted, by duly elected representatives of the People of the United States, in 1970. This group of regulations "require[s] financial institutions, which under the current definition include a broad array of entities, including banks, credit card companies, life insurers, money service businesses and broker-dealers in securities, to report certain transactions to the United States Treasury."