Hey @Zenid,
Personally, I probably go no pic on resumes. I guess it might be different for industries but I generally hear that no pic is preferred. It can reduce bias in selection ad can add unnecessary information on the resume to be parsed as you mentioned. In saying that though, LinkedIn is like a resume and a headshot is favourable on there so in that context (like a digital portfolio, headshot, social media type sort of project) that might make sense. In the traditional resume submission though, I’d say skip it.