It is weird how it works with anyone there but the doctors... Do they have some type of cartel or mafia that nurses and other staff don't have?

They do, it’s called the AMA, American Medical Association. Very tight control of who can be a doctor, how many new doctors per year, etc. which ensures salaries stay high. They also fight against other roles like nurses doing too much doctor-like work, helping doctor pay while harming nursing pay.

At least where I live there’s a shortage of doctors so you can’t negotiate with them . There’s a shortage of nurses too, but if you lose 1 nurse because they’re striking it’s bad but things don’t collapse. With 1 fewer doctor who also knows and is allowed to do things nurse don’t / can’t things get really bad. They also have access to power, are often elected, and are respected.

Nurses need to unionize I think and strike to get something .