A very interesting and understandable argument.
It certainly is odd how Portal is an FPS.
And you described the difference between Battlefield and Call of Duty quite well in my opinion.
Of course some people won't like how you named their genre, but your arguments are quite good.
As for the removal of genres based on presentation, that would be great.
If you are searching for a First Person game where you shoot people, you don't really search for Portal in general.
Such things really need to be sorted out, but is more a problem with what genre the developers give their game.
Portal should be a puzzle game, but with the recent release of multiple puzzle games where you control a character, i think there should be a genre for that.
I don't think the current genres will be changed a lot, but i would certainly support it.