It has to be said that fooling the public in general, strangers with whom you would have limited contact, and fooling someone you work closely with day in and out are different things.
There have been and continue to be people who lead double lives and people close to them are often none the wiser to it. That said those leading those double lives are trying to remain unnoticed and out of sight. That doesn't apply to a superhero who by nature will inevitably come into contact with the public.
A disguise does go beyond mere appearance. For Batman, he operates mostly at night in the shadows and usually ill lighted environments. His other disguise is making certain the Bruce Wayne persona comes across as mostly self-centred and highly unlikely as someone willing to inconvenience himself and certainly not to the extent of endangering himself for the sake of others.
Spider-Man's persona is supposed to be quite different than Peter Parker. Parker is a socially awkward nerd while Spidey is a confident, wise-cracking extrovert. The full face mask doesn't hurt either.
Superman basically hides out in the open. The Clark persona isn't be that different from Peter Parker's other than Clark being a good reporter. Clark just needs to come across as one of the last people who could bring himself to be openly brave and capable. Now that could cut it with most, but not likely with someone like Lois with whom he has a lot of contact with. That's why I think it works in MOS that they got that element out of the way.