Sorry, Kinja was being Kinja and I couldn't update my post at the time, but I wanted to add that I fucking hate the patronizing tone of little "helpful reminders" in women's washrooms, but all the more because I only recently found out how very rare they are in men's washrooms.
There is the universal sign law which argues that a sign only exists because a problem is present. It's often used to refute arguments that women were more "proper" in, say, Victorian times because you wouldn't need to write a treatise like "The Angel in the Home" if women were really that naturally subservient. So arguably women's washrooms are much worse than men's and that's why we get bombarded by passive-aggressive "tips."
But the other option is that mess in women's washrooms is simply less tolerated — we're the fairer sex and, therefore, the cleaner sex. We aren't supposed to be messy or to block toilets or to really admit that anything comes out of our bodies at all.
As a result, we need to be "put in our place," even though, as the respondent points out, a lot of the time mess exists because of poor design or a functional misunderstanding of how our lady business works.