In my world, if you don't ever get married, you will never have sex.
I seriously doubt people would get married just to have sex because of the legal ramifications of marriage, or more specifically the legal ramifications of divorce.
I think it is perfectly feasible in the modern day. It just takes some self control and dedication to ones's values. I think you appreciate it more if you wait until you tie the knot. It means so much more than just the act when it's done in the context of unconditional love in a marriage and not with some drunk chick from MI Tech in the backseat who you will never see again (or want to). The problem is the vast majority of the modern day folks simply want it all now. But it's nothing that is impossible to accomplish (no premarital sex), you just have to want to accomplish it. It's really not that hard.