Removed unneeded override_system_checks

Refs #23685.
Fixed #23653 -- Fixed Windows failure of a logging test added in refs #23569.
Fixed #23663 -- Initialize output streams for BaseCommand in __init__().

This helps with testability of management commands.

Thanks to trac username daveoncode for the report and to
Tim Graham and Claude Paroz for the reviews.
Made testing of stdout and stderr more consistent.

Refs #23663.