If we actually wanted contact tracing to work, we'd go with an all of the above strategy, including telling people when they get their positive test to go ahead and immediately call everyone who they can think of that they've had contact with in the past few days.

Analog contact tracing is great because if the tracer is good, they can help evaluate the risk of a situation -- duration of exposure, mask usage, distance, etc.

Digital contact tracing is great because it can potentially reach people who the case doesn't know personally or have contact information for. You're not going to be able to provide a phone number for the person sitting at the next table at the restaurant.

Self contact tracing is great because it can potentially happen faster.

Of course, in order for contact tracing to have much value, you have to have a place for people to quarantine. That seems to be the missing link in many places. There was just a story in the NYT about an immigrant family who lived in a two bedroom apartment with nine people. The mom caught COVID and tried to isolate by sleeping in the closet, but this was not successful. If governments want to get serious, they need to provide out of home quarantine free of charge. This was very successful in Wuhan as a mandatory program, but IMO you would get good compliance if you just told people that they should go to a free hotel room for two weeks and that meals would be delivered.