FXAA uses around 1 ms on consoles, if it can combined to some existing post processing pass (otherwise it will use around 1.5 ms). Assuming the worst case (1.5 ms), it takes approximate 10% of 60 fps game and 5% of 30 fps game frame budget.
Do you have that much GPU cycles to spend? Would you instead add something else (for example SSAO, more objects, effects or better lighting)? Does your content have lots of subpixel geometry that causes bad shimmering with FXAA (long view range, fences, phone wires, etc)? Does your art style depend on sharp texture details (FXAA slightly blurs high contrast textures)? It's a compromise solution. Most game designers do not want to change their design / art direction (no fences/wires, soft background, etc) because of some arcane technical limitation by a post process AA filter. Technology should enable designers / artists to create the game they want, not limit their creativity. I fully understand why some developers do not want to compromise with FXAA.
We are using FXAA because it suited our game pretty well (there are some problems in further away geometry, but we have soft fog and DOF to minimize the problems). It also was the only antialiasing method we could afford (in a 60 fps game). If we could have afforded better techniques, we would have used them. Console development is all about compromises. I am still not 100% sure FXAA was the right call, because without it we could have afforded a cheap SSAO filter (and the ambient lighting outlook is one of the things I dislike most in our current technology).