A tank's job is to do all of that.
They're supposed to mitigate as much damage as possible (i.e. stay alive and make the healer's jobs easier), and maintain aggro (holding aggro + making the healer's job easier).
If a tank's not holding aggro then your group will fail. If your tank has low damage mitigation and doesn't cycle defensives properly, your group will fail.
Conversely if the healers can't adapt to the situations and keep the group up, then you will obviously fail.
yes a tank is supposed to do all of that, but a tanks PRIORITY is to first make the healers job easier. holding aggro and not dying is a GIVEN, without that you cant even be called a tank, but thats what seperates a good tank from the rest.