They wake up in a white room remembering nothing—

In anime, why are women drawn with such ridiculous and distasteful proportions?

Throughout most of anime this simply isn’t the case. Besides the slight cartoonishness innate to the anime art style, very few characters could be described as having a figure that is not at least possible for regular humans to have.
To memory only a few small sub-genres frequently have humans with unachievable figures, namely ecchi/hentai series where some women may have breast/hip sizes that are not possible.
This is to appeal to specific fetishes, of course.
Another one that comes to mind are series that have muscular male characters whose figure goes far beyond that of realistic possibility, notably Baki the Grappler, and to a lesser extent other series like Jojo’s Bizarre Adventures, DBZ, and Fist of the North Star. Top: Inhuman breasts; Bottom: Inhuman muscles (from Baki the Grappler manga).
These proportions are definitely ridiculous, but whether or not they are distasteful depends on the individual viewer and the goal behind drawing the characters with such ridiculous proportions. The main thing about anime/manga, along with most animations/comics, is that the characters tend to be drawn at the peak of achievable beauty (females) or handsomeness/fitness (males).
People who are below average in these departments are rare, you aren’t going to see that many ugly women or fat men besides those that they are deliberately made that way for comedic effect or to gross the viewer out.
Why is this? Because people would rather look at characters that are sexy, handsome, beautiful, and healthy.
Even background characters are rarely drawn being sub-par in regards to attractiveness.
Viewers simply don’t want to look at series full of ugly/unattractive main characters, this goes back to ancient times where legendary figures would always represent the peak of beauty or physical power. In short, ask yourself this: are any of the following regular anime females “ridiculous” and “distasteful” in proportion? While all these girls are certainly on the high end of the beauty scale, their forms are by no means unachievable, ridiculous, or distasteful.
Frankly I have much more issue with the situations female anime characters get in (ecchi/fanservice scenes) than their physical forms.