Mass executions were even broadcast live on the radio as early as 1941.

This is somewhat misleading and I assume you’re being informed by the wikipedia article?

https://en.wikipedia.org/wiki/Knowledge_of_the_Holocaust_in_Nazi_Germany_and_German-occupied_Europe

Berlin Radio broadcast the mass-execution of Jews in Białystok and the burning of synagogues in July 1941.

The reference cited is a scan of the JTA daily news bulletin 1941-07-18 in which it is stated

In reporting on the execution of Jews in Bilaystock by German soldiers, the Berlin radio stated that a search for arms was conducted by the invading troops in the burning synagogues “where large armament stores were found”.

This isn’t a direct source for the radio broadcast but we can surmise that a person living in Germany at the time, who heard that a search for weapons was conducted and persons executed as a result during war time, may have been misled by the context into believeing that either these executions were not widespread or unlawful.

Not to mention that not everyone would have heard the broadcast to begin with. Media is much more accessible today than it was in 1941.

You need to consider how a reasonable person may interpret such news and the way the news was delivered, propaganda was not (and still isn’t) well understood by the public.

The deportations left paper trails perfectly accessible to any interested member of the public

While there were paper trails these weren’t exactly being handed out to the public, and anyone asking too many questions would have faced suspicion as a spy, traitor, communist or Jewish sympathiser.

and forced labour from the camps became a common sight in public, and with it came the public beatings and summary executions at the hands of their SS overseers.

Executions were typically done out of sight of the general populace, especially at the start.

By painting everyone in Germany as complicit you’re ignoring the reality, that information can be controlled by a Government, that it can skew public perception with propaganda, and that people were often living in fear of their lives by the time they did find out.