How can I enable shell completion after a redirect or pipe? ">"

[brent-spyder]

Take the following command:
my_click_command --foo bar > /tmp/file.txt

I noticed that when bash shell completion is not enabled I get standard shell completion for files/directories. So after the redirect character I can easily output my results to /tmp/file.txt

However, when bash shell completion is installed I get all the completion I would expect in the options of my program, but I lose the native shell completion after a redirect or pipe.

Am I doing something wrong or is this a limitation?