Your post doesn't make sense to me. No matter whether a cable is LV or HV, it has a certain maximum continuous temperature at which it can operate. That temperature will correspond to a certain ampacity. The cable should be protected from long term overloads above its rated ampacity.
Also. most if not all electrical codes are crystal clear on this subject. For example, Canadian Electrical Code Section 36, High-Voltage Installations, Rule 36-204 (1) "each consumer's service, operating unit of apparatus, feeder, and branch circuit shall be provided with overcurrent protection having adequate rating and interrupting capacity in all ungrounded conductors". Overcurrent device is defined in Section 0 as "any device capable of automatically opening an electric circuit, under both predetermined overload and short-circuit conditions...".
Are you thinking of a utility situation where the utility does not have to follow the code? However, you should still follow good engineering practise, which is to provide both overload and short-circuit protection.