As you stated, some of us have a number of styles for different genres set up that we can go to in a hurry ... even if it is not the 'perfect' match for the particular song, usually it is something that will be pretty close ...

Or, if it is a gig where you will be taking an intermission, try to set it up then ...

And if it really impossible to do, well, I feel we can't be expected to play every song ever written on a moments notice ...