I used to be the top-level support escalation at a company, and I made sure to brief all the tier-1 support personnel to escalate directly to me any call using "shibboleet" Sadly no one ever used it.

The company had "Nuclear" in the name, and our average customer had at least a masters in physics, so maybe not the typical support situation. But in at least one case, it has been a real thing. It doesn't work at AT&T and Spectrum, I've tried.

Unfortunately, my experience with customer support at various companies matches exactly your description.

Having heard many other similar stories, I assume that this is really how nowadays typical customer support is, so anything else, if such a thing exists, is a rare exception.