For someone that hasn’t heard of they Mayo Clinic other than through webite articles describing medical conditions, are they that desired/high-quality?

My wife was diagnosed Devic's disease, a rare disease with a grim prognosis. Almost every paper we could find on it had the name of a doctor that worked at the Mayo Clinic in Scottsdale. We lived in Arizona at the time so we went there and found that doctor. He corrected her diagnosis as MS, not Devic's. They both suck but Devic's is much worse. We paid out of pocket and getting the correct diagnosis was worth every penny.

I'm not sure if you live in the United States, but Mayo Clinic is probably a top 5 hospital system in the US. It is legendary. Just read the opening paragraph from Wiki: https://en.wikipedia.org/wiki/Mayo_Clinic

    The Mayo Clinic (/ˈmeɪjoʊ/) is a nonprofit American academic medical center focused on integrated health care, education, and research.[6] It employs over 4,500 physicians and scientists, along with another 58,400 administrative and allied health staff, across three major campuses: Rochester, Minnesota; Jacksonville, Florida; and Phoenix/Scottsdale, Arizona.[7][8] The practice specializes in treating difficult cases through tertiary care and destination medicine. It is home to the top-15 ranked Mayo Clinic Alix School of Medicine in addition to many of the highest regarded residency education programs in the United States.[9][10][11] It spends over $660 million a year on research and has more than 3,000 full-time research personnel.[12][13]

A little deeper:

    Mayo Clinic has ranked number one in the United States for seven consecutive years in U.S. News & World Report's Best Hospitals Honor Roll,[19] maintaining a position at or near the top for more than 35 years.

IIRC, the Mayo Clinic invented the medical checklist. Like, people actually read the checklist and make sure that they tick off all the boxes they are required to tick off.

That's why they are number one. Because they actually use checklists.

"The unreasonable effectiveness of checklists"

In general for US healthcare providers there is little relationship between price and quality. They have to meet certain quality standards in order to operate at all, but outsides few limited areas they don't get paid more for delivering higher quality care. So quality (or lack thereof) tends to come down to organizational culture and management.