Intoxication, i.e. "drunk sex is rape"

Statutes and case law are different in every jurisdiction. But generally speaking, in Anglo common law countries, even severely intoxicated people are legally considered capable of consenting to sex. Consent only comes into question when someone is intoxicated to the point unconsciousness or something close to it; essentially they would have to be unaware that they are having sex, in that moment.

This is consistent with the ordinary understanding of the concept of consent. The fact that alcohol/drugs can alter your cognition and decision-making does not mean that you are considered to be without agency while intoxicated. If I get wasted at a nightclub and blow a load of money on champagne, no one would suggest that the establishment committed theft by selling me champagne while I was drunk. A consensual decision does not need to be "good", "wise", or "rational" it only needs to be made freely.

"Coercion", i.e. "being pressured into sex is rape"

Virtually no legal jurisdiction criminalizes having intercourse after repeated requests. And in the absence of force, threats of violence, or confinement, one can reasonably continue to refuse the requests and/or extricate themselves from the situation. Only when efforts to extricate yourself are impeded would the situation enter truly coercive territory, such as if you are physically blocked or restrained from leaving, or if they are in your home and refuse to leave after being asked.

But agreeing to sex because you're a doormat doesn't make it nonconsensual.

Additionally, acceding to an ultimatum to have sex, where the consequences are non-violent and lawful, is still consensual. If say, your partner threatens to break up with you if you don't have sex with them, that is within their rights because they have no obligation to stay in a relationship with you.