Overcoming an unamendable constitution and necrocracy by drawing up an entirely new constitution is a waste of time and money and opens the door to democratic instability.
If a government has to throw out all aspects of an existing constitution and start again from scratch to make a minor constitutional amendment, the process of updating a constitution would come with substantial risk. Institutions could be undermined, the public could lose faith in the democratic process, and fundamental human rights could be at stake.
This leaves an unacceptable margin for abuse in the amendment process. By undermining human rights, democratic institutes and political stability, unamendable constitutions go against the core values of democracy.