The aim of contact tracing is to lower R0 that way, instead of by lockdown.
Scenario 1: No contact tracing. No lockdown. Person A is infected. They go around for 2 weeks before developing symptoms. In that time, they infect 3 people. R0 = 3.
Scenario 2: Contact tracing. No lockdown. Person A is infected. However, the person who infected them gets tested, and a list is formed, either through memory, or by technology, of all the people they spent much time with. Person A is contacted 2 days after they contracted the virus. In this time they have only infected 1 person, instead of 2. R0 = 1.
Obviously, the figures are not just 1 (cases remain steady) or 3 (exponential growth), but this is basically how tracing acts as an alternative to lockdown. Not every infected contact will be found, but if it is done well enough, it will keep r0 below 1 without any need for lockdown at all.
Tracing can only work when you have a relatively small amount of cases, because it is very labour intensive. But it DOES work, and is doing in several countries around the world.
How much you can ease up on other measures, like allowing kids back at school without any distancing at all, cramming people onto public transport, I don't know. It might not permit absolutely everything to go back to normal. But it would certainly allow us to live a lot more freely than we are now.