Question

Is it desirable to eliminate natural unemployment? Why or why not?

Short answer

It is desirable for workers to eliminate natural unemployment as anyone who deems it economically viable to work will have a job. Additionally, no unemployment will give laborers more bargaining power as it will be hard for employers to replace them with someone else.
It is not desirable to eliminate natural unemployment for the economy because then there will be no scope to expand the business. It'll become more costly for firms to attract employees, this will require them to allocate more resources to labor which will diminish investments and expansion.

Step-by-step solution

Step 1. Natural Unemployment.

The natural rate of unemployment is the unemployment exisitng despite the economy being stable and growing.

Step 2. Eliminate Natural Unemployment.

It is desirable for workers to eliminate natural unemployment as anyone who deems it economically viable to work will have a job. Additionally, no unemployment will give laborers more bargaining power as it will be hard for employers to replace them with someone else.
It is not desirable to eliminate natural unemployment for the economy because then there will be no scope to expand the business. It'll become more costly for firms to attract employees, this will require them to allocate more resources to labor which will diminish investments and expansion.