I see your point broadly, but I think it's possible for that to be true and to also take university-grad H1-B employees.
That's false. Maybe this was true in the past.
First, they cannot self-sponsor. Which means that the hypothetical company would have to apply as soon as they step foot on US soil. There are no incentives to do so and incentives against it. So they generally won't.
Expect the process to start a couple of years before the H1B visa is set to expire.
Even if started immediately, just for processing time alone you are looking at around 2 years. 2 to 6 months for the PERM process. I-140, similar. The AOS stage can take 10 (or more!) months to process. The last two can be filed concurrently. It's still one year on the absolute best case with no RFEs or audits whatsoever, counting from the moment the application was filed, assuming all documentation is instantly available (like employment verification letters from past workers, translations etc) and assuming lawyer time is zero (which obviously is not the case).
Of course, if you are Indian or Chinese, add years or decades to the above.
My understanding (I have always been a citizen of the US) is that the processing time to get a green card if you are Indian is so long it might as well not be an option.
It’ll never clear without reform.