i do not do the egg one but i do milk for water and butter for oil for both cakes and brownies and its very good. i second the idea that it is not wise for cookies.
i would also throw in the idea of instant coffee in the brownies, its fantastic. double dark chocolate expresso brownies are the only reason my coworkers tolerate me i think.
i legit do this all the time, except the add an egg part, but theres no way that would ruin anything, not sure what the overall effect would be but no way it would ruin anything.
Thank you