Is there some rule that says other people aren't allowed to pursue a green card? That doesn't seem like a differentiator to me.

That's a real question, I have no idea how any of it really works in the practical sense.

Yeah, see https://en.m.wikipedia.org/wiki/Dual_intent

> Persons with H-1B visas (for specialty workers and their spouses and minor children with H-4 visas), K visas (for fiancees or foreign spouses of US citizens and their minor children), L visas (for corporate transferees and their spouses and minor children), and V visas (spouses and minor children of lawful permanent residents) are permitted to have dual intent under the Immigration and Nationality Act.[1]

> Most other foreign visitors and workers, like those on H-2B worker, H-3 trainee/worker, B-1 business, B-2 tourist, Visa Waiver Program visitor, F-1 student, J-1 exchange visitor, M-1 student, journalism, and entertainer visas should not have immigrant intent. Such visa holders can be denied admission if the consular or port official reasonably believes that they have interest in permanently remaining in the United States (i.e., in pursuing a green card).

Yes, there are visas Like L1 Visa where you can work in US but never apply for a Green Card, and this is considered a non immigrant visa while H1b is considered a dual intent visa. Which is why regularly people who come in on L1, separately participate in the H1b lottery!

TN can’t