Incorrect. After implementing a lockdown, and getting R<1, essentially brings you back to square one. That's when contact tracing is implemented and lockdown ends. The contact tracing will keep R<1 until a vaccine/better treatments/ICU's are implemented. A secondary lockdown might be needed in case people another outbreak occurs.
The feasibility of contact tracing has nothing to do with the R. It's practicality is purely based upon your ability to contact people who are infected.
Sure, tech tools that automate part of that process, increase that number - maybe even benefit more rural place - but if you launched it in NYC right now, it'll just notify literally everyone in the city, day one. That's not useful.
Probably, but the news media in Western countries - particularly the US and UK - have been pushing the narrative that it's essential for, basically, partisan political reasons. In the US, it's being used as part of the attack on Trump over the CDC screwing up testing because the media doesn't like him, whereas in the UK it's part of a narrative that the reason we stopped contact tracing is part of a plot by our government to kill the elderly. In both cases, it's basically intended to create the perception that the ruling political party killed huge numbers of people. If it causes other countries to do stupid, counterproductive things that's just collateral damage.
Meanwhile, China has been pushing the claim that they contained Covid-19 via contact tracing and testing as part of the "model for the rest of the world" narrative they're using to fight domestic anger at their handling of the outbreak, with the WHO's help. (This does not seem to be an accurate description of what they actually did to contain it.)
It'll be good for the next pandemic - but not this one.
Over the next 12 months, we should focus on how we change society to be more sanitary, in general.