If you are a performer of any kind in any venu, it seems to me a head shot is needed. Even writers seem to need them, since all publicity generally contains a picture unless, of course, you are Thomas Pynchon.
As to jobs where looks should not matter, it seems to me that people would put their photo on the resume only if they thought they needed help. I.e., they would probably think they were pretty hot, and that their looks might sway someone in their direction all else being equal. Personally, I don’t like that kind of thinking, and I would be less like to hire someone who put their picture on the resume, all else being equal.
Sometimes a good looking person happen to be the best of a group of applicants. It would be a shame to lose them or have to not choose them due to the photo. But my assumption is that anyone put their photo on the resume, it’s because they have a weakness they don’t want me to discover.
I also think that only hot looking people would put a photo on the resume. To me, that suggests something of an attitude about looks. A lack of humility. It’s not a trait I like to see among job applicants.
Finally, it’s just plain obnoxious. Just obnoxious. It turns things into a beauty pageant instead of a competition based on skills. I don’t really enjoy working with obnoxious people. So perhaps they should do me a favor and put their pictures on the top. Then I know who they are and I can throw the resume out without even reading it. Fortunately, I have never seen a resume with a picture on it.