The Hulk is a pretty bad example since he has no skills at all. (I also argue he's not a superhero, but that's a discussion for another day.)
I think that the MA is a yes, but it can be represented in so many ways. A lot of the non-fighting types will still have some basic form of self defense training resulting in a minimum of:
Breakfall
+1 w/ Strike or Block
There are too many examples of characters that are completely ignorant of their home cities (either lazy or brand new) to consider AK: City essential IMMO. Likewise, day job skills aren't essential. In fact, I can think of a whole slough of recommended skills, especially for the good, prepared hero, but a lot of rookies blow the curve (which is what makes them interesting).
Not very helpful, probably, but I think we should define a certain type or style of hero first. Rookies vs. veterans, self made vs. powered, crime-fighters vs. world savers, etc.