The six month moratorium on applying to internal positions is bad for the company, but good for her.
This is a really, really big (and likely incorrect) assumption. As someone who has managed a customer service department, it's pretty obvious you've never actually run a department (not meant as a slight, but an observation). It's far more complicated than it looks from the outside, particularly when it is managed competently (good managers make management look simple and easy, but it is anything but).
The company likely spent a large amount of money hiring that employee (advertising, screening, interviewing, recruiter fees, training, etc.). They need time to recoup that investment. My rough break-even on an employee generating a RoI was about 2 years! You spend money hiring, then you're paying salary for "sub-par" work (they're not earning their keep as they train, learn systems, soak up time from experienced folks, make mistakes (learning opportunities), etc.), then you're paying salary for "par" work, then you're finally earning back the initial investment with above average work. Sure, it's better for them to turn-over internally, but it's not really that much less expensive to hire internally. The new department gets a slightly faster RoI and slightly lower risk (good at customer service may not translate into good at accounting, software development, marketing, etc.), but the customer service department lost money on the deal and has to start over with a new hiring process.
If you have high turn-over within a department, you're constantly in those "sub-par" and "par" phases and the customer service organization is hemorrhaging money for below average service. Depending on the organization/industry, customer service is one of the most critical components of customer retention and/or return business. Depending on budgeting, metrics, employee comp plans, the manager might be in "hot water" because her department is over budget and under performing.
The other unintended side-effect of the customer service as a stepping stone into "more skilled roles" is the attitude that creates within the customer service department. People don't want to be there, they don't see a future there, they don't feel appreciated for their work and skills. Your best employees want to get out into the "glory" positions within the company or worse, leave the company for another customer service job that is better appreciated/supported.
She wants her department to be respected.
Start by learning to respect her department.
It's obvious from your question that you don't like customer service work, and as a result don't value it ("more skilled roles", "certainly in any customer service situation, six months is a long time", the idea that there is no career growth in customer service).
- Customer Service is an extremely skillful position. It's really hard to handle difficult customers. You have to be knowledgeable, good at thinking on your feet, diplomatic, etc.
- Six months is a long time to do something you hate, and you shouldn't accept a job you're going to hate. But if you like or are ambivalent about your job, 6 months is no time at all.
- Customer Service should absolutely have a career path beyond Customer Service Rep I. It can go into content creation (FAQs, manuals, webinars, videos), training, consulting, etc. My department's "rock star" employees were making comparable salaries to our "rock star" developers. If your company doesn't have a natural career path within customer service, that's a far better answer to the perceived problem.