Uh, no.
Relationships and marriage are becoming trash in America because men are marrying women that don't respect them.. Don't even really like them, and women are pretending this is normal.. Like they aren't even supposed to be "in love" with their husbands. It's wrong. Women, for their own sexual greed, want to seperate sex from serious relationships. They want to get their brains pounded out and have "good sex" until they have had enough, then get married. This isn't a cool world.
Seriously date somebody you have sexual chemistry with. Sex bonds humans together. All this separation of sex from actual relationships is poisoning the Wests culture.
If you are the "cool" guy she puts out to right away, you might always be the cool guy to her. Then things have a chance to work.

THAT is why relationships are trash in America? because women don't respect men? lolwut? who hurt you?
There are a whole host of reasons to describe how relationships got to be how they are, and it isn't just between men and women.
Relationships, ALL of them have been on the decline. There are a lot of different reasons for that. MANY people are simply shitty communicators, whether it be between them and their partners, or between them and family members, coworkers, and strangers on the streets.
You have a very simplistic view of relationships, sex, and what sex means to individuals, and how men and women perceive sex.
Men and women tend to think about sex in very different ways, and it definitley isn't simply about "get their brains pounded" out for women. lol
And deciding whether or not a relationship is worthy or not on whether she puts out as fast as she did with the last "cool guy" is terrible, juvenile advice. Sex can be a lot more complicated for a woman, and her putting out quickly does not automatically mean she did it because she liked you. You can pressure a girl into sex pretty easily, she could be feeling lonely/sad/depressed and is just doing it, she could simply just be doing it because she doesn't want to disappoint you, she could be bored, etc, etc--girls fuck for a lot of other reasons that men don't
Sex is important to a relationship. I don't disagree with that. But it generally means something different for us than it does with women. Not 100% different, but there is definitely a different view of it.