Support shipping of Console.xxx calls at App Insights

Is your feature request related to a problem? Please describe.
We recently implemented front-end application insights with the requirement that we ship all console logs to application insights. This doesn't appear to be possible with the base library.

Describe the solution you'd like
We would like the ability to ship console logs to app insights using the base library. Of course, we'd expect this to be configurable, and the default behaviour probably to be don't ship.

Describe alternatives you've considered
As you can imagine, we achieved this via console method overrides, which works just fine.

Additional context
This is by no means a bugbear, as our implementation was straightforward - it's just a suggestion.
It's possible this isn't a high demand requirement. But it may also be fairly trivial to include and would be an improvement to the library.
I would also expect may have has been discussed and intentionally excluded as a feature, in which case it would be great to know the reasoning for that decision.

The issue names no files or tests; start by reviewing the base library's console handling and configuration surface, then compare the console method overrides described in the report. Done means console calls can be sent to Application Insights through an opt-in configuration, with shipping disabled by default.