No, it's not a "common myth", it's the truth. You can't get consent if the person is sufficiently drunk.
This is not true in the UK, at least.
Now, the next day, the person might not mind the drunken sex. It might be the start of a fling (especially if the people were jonesing for each other anyway). But, there was no consent. This means that if the person DOES mind (the next morning) that the sexual contact occured, then the law is quite willing to step in and ruin people's lives.
If the person cannot consent, then the act is illegal whether or not the person minds. Whether it is rape or not is not decided depending on whether the person regrets it the next morning! That's yet another rape myth.
People can be prosecuted even if the person doesn't press charges (and there's good reason for this - the victim may be afraid of doing so, but the criminal is still a danger to society). Consider underage sex - the person can't consent, and it's illegal whether or not the person says they minded. Also S&M is illegal in the UK, because you can't consent to assault for the purpose of pleasure - in the Spanner case, people were sent to prison even though they stood in court and said they wanted it.
Saying that people can't consent when drunk means that adults can't have sex when drunk. It would be illegal for them to do so.
And even if it wasn't common to prosecute unless the person pressed charges, it still means that whenever two adults choose to drink and have sex, they are gambling with their liberty (e.g., imagine people in a long term relationship, but later they fall out, and one of them decides they didn't want it, making it rape). Do we set a time limit as to how long after the person can retroactively decide it was rape or not?
The laws have become quite harsh, because people were using the "but I was drunk too!" excuse too much.
I'm not sure I understand - what if both people were drunk? Are they both guilty, or neither, or only one of them? What if the man's drunk but not the woman?
There are other problems too - how does someone who wants to be law abiding know how much someone else has drunk? Do we need breathlysers?
Just like with drunk driving, society has become harsher with holding you accountable for your actions.
Hang on, with drink driving, it's the person who gets drunk that is punished, because of the danger they pose to others. If it's really just like drunk driving, then it's the drunk person who then has sex who should be prosecuted...
You did not legally consent. Legally being the key word. "Rape" is partially in the mind (whether you consider yourself to be a victim). If you feel that you actually were okay with the sex, then don't press charges. It's quite simple.
Whether it's rape or not is in the mind? That's not a good way of deciding the law. So does it become rape if woody60707 now decides it was rape after all?