I wouldn’t generalize it so much. Yes “full stack” is pretty bad to describe many jobs people do. But when you work for a startup and you are needed for anything that can com up that is your job. Although I am just starting out and have that “laundry list” of experience I do still keep up with almost all that experience do to my side projects and job.
I would however rather call myself a software engineer but my job description is Full Stack Developer according to the company I work for.