Gents,
I think the point that is being missed here is that we tend to use the MCB as a combined overload/short circuit protective device. We often combine these functions into one device but we don't have to.
Sometimes overload protection could be omitted. Consider the immersion heater - its rated at, say, 3kW ie 13.04A @ 230V. Now, this device is either going to be functional or faulty. If its functional, it isn't going to suddenly start to pull, say, 19A - it can't. It cannot overload its circuit so we dont need to provide overload protection. We do, however, still need to provide short circuit protection. If its faulty then it will most likely fail short circuit or fail to earth.
If it fails short circuit then the current which flows will be limited by the impedance of the circuit & will approach the Psc - this will be several hundred amps. If it fails to earth, then if the installation is TNCS or TNS then the earth fault current will approach the short circuit current. If TT then the RCD should operate & the MCB would prob never operate anyway.
This is the reasoning behind saying that the protective device is to protect the cable - since by the time it is called into service the device has failed anyway - we just need to protect the cable from damage caused by the fault current.
Obviously, overload protection cant be omitted from any circuit which is liable to overload - ie. the load is not fixed at design time, such as circuits containing socket outlets.
If one studies the characteristic of an MCB one can see where these two functions have been combined, the instantaneous portion (the magnetic trip ie. shot circuit protection) is defined by the letter (eg. B, C, D etc), the overload portion is defined by the number, eg 16. The 16 bit operates on an IDMT curve such that the greater the load current is obove the rating, the faster that the device will operate until the instantaneous part takes over.