Hello, I understand your concern, but would like to point out that Mayo uses a treatment model that is somewhat different than most specialty clinics. While you may be assigned to an asthma specialist as your primary doctor, they will consult with/refer you to any other doctor or department as needed to treat you.
Have they explained to you how the process works for new patients?

My brother is a Mayo pulmonology patient (different diagnosis) who was seen/tested extensively at Mayo before he was referred to his current team. Due to their high level of specialization, they only see a very select group of patients once determined their exact skills are needed. Even with that, he is only seen by them once a year or during a crisis, the rest of the time his care is managed by a pulmonologist near his home, who consult with Mayo if needed.

The high demand for treatment, coupled with the scarcity of docs in certain specialties, means this model can provide the best care for the most people.
Sue