Ombudsman services are able to resolve conflicts where the customer and business don't agree. They're appropriate for regulated businesses to draw a line in the sand as to what is a legitimate complaint by independently settling cases where the customer and business did not agree. If the Ombudsman hears 100 unresolved complaints and upholds only one then probably the ordinary customer services are working as intended. If they uphold ninety nine something is gravely wrong with your customer services and the regulator needs to step in.

This isn't so dissimilar from the method used in pathology to deliver consistency in results across multiple labs and assay methods. You identify some boundary cases. This is definitely normal, this is definitely cancer but this is borderline, repeat a few times. You replicate and get all the labs to mark your samples. Then you can identify labs (or assay techniques) that aren't reliably putting things in the right categories and demand they improve or stop.

I've worked for various technical help desks over the past 20 years and I'm saying that if a help desk is setup properly, ombudsman services become unnecessary.

A big part of this is how empowered you make your various levels. The SLAs I've always worked with, created, and worked under measured time on calls and customer satisfaction was always one of the more important measurements.

You could also think of it as a "priority lane" for support. Pay nothing, get whoever for support. Pay $x, complaint goes to an engineer. Pay $y, the product manager. Etc. Skips the middleman process for customers that are in a rush.

If a customer is willing to put up 10k to get their issue resolved, it's probably an issue worth resolving.