Use hardware that is not present (such as high end GPUs) in the standard configuration
Need to run software that requires administrative privileges
Have a job where visual quality is crucial (photo or video editing) – RDP compression compromises that
Have a job that routinely involves installing software (product evaluation, competitive analysis)
Need a type of computer that is not otherwise used in the business (Mac or Linux in a Windows shop)
Use multiple displays (multiple display support in thin clients is improving but may not be sufficient for all)
Make intense use of video (video editing, game development)
Interface with hardware with no network capabilities (scanners, lab equipment, badge printers, etc)
Develop hardware (computer is interfaced with things under development)

In some cases, it may make sense to give those users a thin client that is used for routine job functions (reading and sending company messages, logging time worked, etc) as well as a separate computer that is only used for running things that fall outside the capabilities of the thin client. It’s especially important to get IT staff to use the thin clients for some of their work, even though other parts of their job requires doing things that are outside its capabilities, so that they will be familiar with its capabilities, performance, and limitations.

I agree 100%. I also agree it would be worth doing even if you didn’t save on hardware for exactly those reasons. I’ve seen how stretched thin desktop support resources are. And data is a company’s most valuable resource. I can think of one company I’ve worked with whose business is all B2B so they’ve never sold anything to you or me directly, but if their data were stolen, they could lose competitive advantage.