If customer support employees don't want to deal with angry customers they should take a job whose purpose is not dealing with unhappy customers. If you as a company have too many angry customers the response should be to fix your product/service, not to find excuses to ignore those customers.

All you're doing to forcing your customers to find other ways to fix their problems - either by finding someone higher paid than customer support and wasting their time instead or by going to a competitor and telling everyone to do the same.