Yeah that sounds pretty unethical but who is recommending such a coach in the first place?
I would also add that in any field the "teacher-student" dynamic is a two way street. The best coach/teacher in the world cannot do much for you, if you are not prepared to put in some effort.
So how many "past students" are we talking about here? If it's just a handful then maybe they just didn't put in much effort or gave up etc...
Also. how are we defining "Significantly improved" ?
But in general I'd say that if it's dozens of students and none of them have improved beyond beginner/intermediate stage then yeah it's probably down to the coaching when all is said and done
Is a prospective chess coach acting ethically if they offer their services for pay, knowing that not one past student has significantly improved their ratings over a period of time.