I like a hybrid approach. I think that at some point during dating, the couple should be having discussions about whether they would be a good match for each other for marriage. Do they have similar ideas about having children, raising children, religion, fidelity, etc. If one member of the couple wants to be in a marriage within, say, a couple of years, while the other is happy to keep dating indefinitely, then the one who is looking for marriage can then know that they are not in a suitable match and can exit, and move on to finding a better match. If they are both interested in marriage, then, by discussing it, they can know that they are a possible good match for each other and can then explore that more completely. If neither is interested in marriage and they want to just keep dating, then that's fine too.
Every couple can make their own decisions. Personally I do not think I would propose to a man, but if we were dating seriously and he seemed to be taking "too long" then I don't know if I would try to put pressure on him. I would be worried that being pressured into proposing would signal he was not really that interested in marrying me. But I also wouldn't feel obligated to stay in the relationship while he took his sweet time and enjoyed my attention and care. I would probably move on, i.e. break up and look for someone else.
I feel that many of the threads on this board indicate that sleeping with a man, without the financial protection of marriage, can place a woman in a very difficult position if she becomes pregnant while they are unmarried. This seems to have happened even to women who were in long term relationships with men who said they were totally committed to the relationship. Where the man showed his true (stingy, or selfish) colors after children arrived, or the couple were together for many years without marriage and then the relationship broke down and the woman was left with no legal right to the home or savings because they were unmarried. So, personally, I would not want a relationship to go on so long that I "ended up" having children with the man, but without the financial protections of marriage.