cause of death button, would be helpful so that families can track so many items like disease, mental health...etc
If you feel the need to add such detail, you can already do so: adding cause of death to the "Reason" field for the Death vital, as a Custom Fact (under Other Information) or even as a Note in the Collaboration section.
However, you should bear in mind this is a SHARED tree, and that (other) close relatives of the deceased might not be as happy as you to have the cause of death displayed so openly. Okay for a relative who died over a hundred years ago, but what about a relative who died quite recently - perhaps through taking their own life? Should FamilySearch really be making it easier to highlight such a fact by adding an additional feature, viz. a "cause of death button"?
I support this request. I would add a "Cause of Death" field in the Death event that is active only if not living.
"Cause" is already a qualifier in GEDCOM X, so this isn't a barrier to addition of this data to the API.