With your flanger experiment you are talking about a mono in, stereo out effect. If you recorded through this type of effect hardware yes you would output the effect to 2 channels of your mixer and pan them hard L and hard R. or send them to a group.
You are still asking why use a mono track and the reason is the dynamic effects. When I mix a vocal before it gets to any stereo type effects reverb or delay it often goes through a filter, compressor, EQ and tape saturation all of which I want to keep in mono. When I want to go to the stereo type effects stereo groups and sends is the way to go.
Just for interesting reading here is a couple of links on this subject.
http://www.homestudiocorner.com/stereo-or-mono/
Anyway I have put too much time into this now and I wish you happy music making.
Regards Ian.