The rhetoric dials up and says, "Instead of telling women to be careful and cautious, we should simply teach men to not rape." 

This would understandable and likely effective if "men" raped but men don't rape.  Rapists rape.  Do the vast majority of rapists happen to be men?  Yes, but the vast majority of men do not rape. 

No one would suggest that we stop telling children to be careful around strangers and instead simply tell strangers "Don't kidnap children" and expect any results. 

No one could reasonably expect anything but the side eye for suggesting that banks forego all of that security they spend money on and instead simply admonish people to "Don't Steal."

The common sense approach includes both specific legislative measures to more effectively punish those who rape and protect those who have been raped from further trauma.  

• If you have been raped, report it immediately.
• If someone is accused of rape, both the accused and accuser's personal identities should be kept sealed until a verdict is declared.  If the accused is acquitted, the names should be expunged.
• The accuser's personal history has NOTHING to do with the alleged crime.  Defense attorney's should be categorically barred from introducing it.
• Rape is an assaultive crime an, aside from medical bills associated with the crime, no financial penalties paid to the victim should be allowed under any circumstances.  This prevents the possibility of accuser's falsely claiming a famous and wealthy person raped them for monetary gain.
• The penalty for being found guilty of rape should be severe and on par with murder as a life has been destroyed.
• Women are the most vulnerable to being raped therefore need to protect themselves and be in control of the circumstances as much as is possible.

"Don't Rape" is as ineffective as telling people "Don't Do Drugs" or "Don't Lie" or "Don't Shoot Guns at Other People."