Why does After Effects not enable me to work with 60FPS?
Those "options" are just convenient presets. Just select Custom and input the frame rate and any other parameters you want.

Of course, if only some of your shots are 60fps, and your final output is 24 or 30 fps, then set your comp settings to the desired output values, and interpret your footage as 60 fps (if it isn't sensed by AE automatically).