These are not meant for people to stay here. There are other paths for legal, up front, immigration.
Students and H1-Bs are not immigrants. They are temporary and for a set time period and purpose.
My wife and I know people who overstayed student visas, and they know they were supposed to leave, back then.
If you got hired on a student visa, that process now requires an H1-B from a student visa conversion, posting for it, after getting some expected - mandated - education, while in the US.
No, we do not need any H1-B or student visa conversions to such H1-B visas. There is nothing an American can't do, as you also noted, by stating you worked with a ton of US citizens in your jobs. You were just another cog in the machine.
We have no lack of cogs.
I did NOT want to stay here. In 1960 era student visa holders were allowed to work max 18 months after graduation if work was in related field as study. Since I spent my own money at the university (actually my parents money, I was only 20 years old in 1960) I accepted a job offer from Link-Belt company in Chicago, to recuperate my college expenses in United States. When my 18 months work about to expire, I gave 2 weeks notice to quit. My employer wanted me to keep working. Their lawyers worked with immigration to change my student visa to permanent resident visa. I could not have done it without company sponsorship. Then I met an American woman, we got married and I decided to stay. Marriage would also have made me eligible for immigrant visa.