The correct answer to this open question is the following.
Although there are no options attached we can say the following.
If there was another Pharaoh would the mummification process still go on?
No, not anymore. The reason why is that the mummification process was a belief of ancient Egypt, in the times of the Pharaohs.
Would the process change towards new rules?
Probably, because modern technology and medical advancements would recommend something different, but as I wrote above, mummification was a belief system of thousands of years ago.
Ancient Egyptians used the mummification process because they believed the body should arrive in the afterlife safely and intact.
The purpose of mummification was to preserve the body afterlife.
Egyptian Pharaohs were considered the representant of the gods incarnated on Earth. People believed they were the representatives of the gods. In the Egyptian Book of the Death, it is described the afterlife path to heaven, to the house of the gods. So the Pharoh had to be mummified in order to preserve his body and use it again afterlife in his path to get to heaven.