If you’re worried about appearing cheap, to people who visit your house, particularly the type of people that might judge a person for appearing cheap, and the opinion of that type of person matters to you, then yes, buy a headboard. Or, if this is like a survey and you’re asking for everyone’s individual opinion, I personally would not judge you as “cheap” for this, but everyone’s threshold for these things is different.
If you’re worried about appearing cheap, to people who visit your house, particularly the type of people that might judge a person for appearing cheap, and the opinion of that type of person matters to you, then yes, buy a headboard. Or, if this is like a survey and you’re asking for everyone’s individual opinion, I personally would not judge you as “cheap” for this, but everyone’s threshold for these things is different.