I don't get "Most eligible bachelor" being used to mean "Highly-desired"

In most usage, "eligible" means accessible/available for something. "Most eligible" in this context should basically translate to "Desperate bachelor who is at no risk of ever getting tied down"

@MikeOShay my thought is that they don't have downsides.

Other bachelors have things that make them less eligible.

@Wearwolf Yeah but that makes them less eligible to be a bachelor. "Most eligible dating prospect" absolutely, but bachelorhood is defined as being single, so they're by definition worse at being a bachelor
@MikeOShay yes, that is unfortunate wording. The bachelor who is most eligible for not being a bachelor anymore