> The death rates in these countries also peaked about two weeks into lockdown, way too soon for lockdown to have had any impact.
On the contrary, that's exactly what you'd see if lockdown had maximum effect.
Suppose lockdown were totally effective, such that nobody contracted a new infection of the disease after policies become effective. In that best-case situation, the medical system would still have to deal with everyone who contracted the illness up to this point.
Because the virus spreads exponentially, the curve of "newly-contracted infections" would come to a peak just before lockdown and then fall to zero afterwards. Those cases would then go through their normal progression, and some would die -- about two weeks after contracting the illness.
This single observation isn't enough to conclude that lockdown is effective since it doesn't rule out other possibilities for a declining death rate (medical treatments, bad reporting, etc), but it's certainly not evidence against the efficacy of lockdown policies.
> The death rates are also following a similar bell curve across the world, seemingly independent of any lockdown policy.
A "bell curve" for disease progression implies a typical logistic curve for the number of total cases. That in turn implies that the community is nearing a 'herd immunity' level.
No nation in the world has anywhere near 'herd immunity' yet. With the highly-transmissible nature of nCoV, more than half of a population would need to be infected to confer herd immunity.
> The countries that have done well implemented test and trace early,
The problem here is that you can't implement test and trace late. Public health officials have a finite contact-tracing capability. One community transmission exceeds this threshold, the only tool left is lockdown -- specifically to reduce transmission down to the point where tracing is again possible.