I'm sure you know this but there is often general confusion about this subject. They are all legally 501(c)(3) charitable organizations. They are all "non-profits". "Not-for-profits" generally means the the subject isn't a separate legal entity. "Charitable" has specific legal understanding, for instance, as something whose purpose is advancing science or education.
No successfully operating non-profit organization does not have operational revenues that exceed expenses in most years. The difference is how those excess revenues are used, not how big the excess revenue is. Excess revenues for non-profits can't benefit private entities, individuals, or shareholders. The excess revenues are generally plowed back into the organization or donated to other charities. It also does not mean that non-profits can't have employees that are compensated commiserate with their positions, even if that means they command very large salaries. And for sure, if non-profits don't have excess revenue over expenses, they cease to function quickly.
Pitt, UPMC, and Highmark are really non-profits, legally and operationally, and they have withstood every legal challenge. They're very large non-profits, each with large scopes, and multiple diverse missions, and therefore have very large operational revenues, bureaucracies, impacts, and flaws, which makes them feel different if you are comparing to a local church or soup kitchen. They also operate for-profit subsidiaries that pay taxes.
No matter how one feels about it, labels and operational motives assigned to them by personal opinions don't change their status.