I don't think it is a sexist assumption, it is what I have observed in reality.
Most women who would like to get married are not actually sitting around reading wedding magazines and dropping heavy hints about what kind of diamonds they like, they are getting on with their lives. Unless they are already over a certain age and want marriage and then children, in which case they might be thinking about it a little bit more, particularly in terms of whether marriage and kids with their current partner is on the cards.
Most men who are actually enthusiastic about getting married will ask the woman before she gets to the point where she feels she needs to bring the subject up. And in most cases they will have discussed it together anyway so only the timing of the proposal comes as a surprise.
I think the way I see it is this. For all women who want to get married, the time in their relationship before they get engaged is at one of three stages.
Stage 1: It's still early on in the relationship, even if the woman is willing to propose to the man she is unlikely to do so because it's still pretty new and she knows most people would think of her as crazy for proposing at that stage.
Stage 2: They've been together for a while, it would be considered a perfectly normal time to get engaged, but equally, they haven't been together for so long that not being engaged yet is weird.
Stage 3: They've been together for ages and she would like them to be engaged already but they're not.
In my experience if a man is enthusiastic about getting married then either he will ask the question or they will just naturally discuss getting married and decide to do it in either Stage 1 or Stage 2, and Stage 3 will never happen.
Stage 3 is where men who don't really want to get married hang out.