It’s not strictly about the words in those exceptions.
In the case of fraud, it’s not the speech itself, it’s the part where someone gives you money (or other consideration) under some agreement or understanding, and doesn’t actually get what was promised. There’s nothing intrinsically wrong with what you promised, it’s your failure to deliver.
Threatening people? The illegal part is not that you used words at them specifically, it’s that you caused them to credibly fear for their life and safety. You could just as well do that without words, just standing outside their place with a baseball bat making menacing gestures. Harassment similarly may use words, but the objectionable part is often subjecting them to your words or actions or presence directly, to cause distress, instead of leaving them alone in peace.
“Hate speech” as a problem generally is about the content of the speech itself. You might wish to convince people that others in a group are bad and worthy of being considered bad. Your audience is typically people like yourself, or third parties who you wish to sway, and if you are in a public place you are mostly not following around an individual to be hated, or telling them you are about to do them violence. (If you do, it may in fact be harassment or intimidation.)
Given that some things that don't use words—for instance, art, money—have been ruled as being considered equivalent to speech for the purposes of First Amendment protections, I don't think the rationale you give there is likely to be the one used to justify the listed exceptions to the First Amendment.
In all the cases listed, the speech in question is being used to directly and (at least usually) intentionally harm or interfere with another person. I believe this is a case where looking to the Framers' intent rather than the strict wording of the amendment is worthwhile in determining how best to apply it. It seems obvious that they did not intend to make all forms of fraud and threats legal with no recourse (and I imagine there is some jurisprudence that cites specifics to this effect).
In the case of fraud, it’s not the speech itself, it’s the part where someone gives you money (or other consideration) under some agreement or understanding, and doesn’t actually get what was promised. There’s nothing intrinsically wrong with what you promised, it’s your failure to deliver.
Threatening people? The illegal part is not that you used words at them specifically, it’s that you caused them to credibly fear for their life and safety. You could just as well do that without words, just standing outside their place with a baseball bat making menacing gestures. Harassment similarly may use words, but the objectionable part is often subjecting them to your words or actions or presence directly, to cause distress, instead of leaving them alone in peace.
“Hate speech” as a problem generally is about the content of the speech itself. You might wish to convince people that others in a group are bad and worthy of being considered bad. Your audience is typically people like yourself, or third parties who you wish to sway, and if you are in a public place you are mostly not following around an individual to be hated, or telling them you are about to do them violence. (If you do, it may in fact be harassment or intimidation.)