In which case it will run the same code, reprogramming CLKPR every time.
This is a good point. So, the CLKPR Register is not required to be of non-volatile and EEPROM type. But, there is a write cycle time; if it would be a normal register, then why is there the need of this write cycle time which is about 0.25 us -- very very very low compare to 5 ms write cycle time of the normal EEPROM.