If a company’s marketing department can’t propose any new opportunities, they should be fired. do you agree?

Yes I Agree 

I do not agree . Because marketing is the main department in a company and has no end . It is technically not possible for a marketing department not to have any proposition . This is the most strategic department in the company and always creates new brands , analyses consumer trends , organizes events ,conducts campaigns ,  searches for new markets , works with R&D department to create new products , changes packaging and offers , conducts all7p process etc....... . Marketing department has strategic , tactical and operational plans for1 ,5 and10 years . So your question is not rational and realistic . Marketing efforts never stops or ends in a company . 

But there are always opportunities!  Just look at the new products that continue to appear in catalogs such as Sharper Image or Innovation or Fascination. Any company with a product or service should be able to think of new ways to modify it, combine it, offer different sizes, or add new features or services. 

Not only can an offering be reshaped for different markets but the offering can also be seen in a new context.

So, I agree with the proposition.