Yes, I agree, they should list the strap size. I honestly wouldn't know what size a "ladies" what strap would be. A quick Google search has results saying stuff like:
"For women, the standard is between 6 3/4 inches and 8 inches, depending on the style and manufacturer. For men, the standard watch band measures between 7 3/4 inches and 9 1/2 inches, again, depending on the style and manufacturer. Watches are manufactured to fit the majority of people."
But, different sites say different things, so I don't think there's really a standard. I have a 6.5" wrist, so even if they listed it as a "ladies watch" I still wouldn't know if it would fit me considering there's such a wide size range the strap could be. As you said, I think the better solution would just be to post the strap sizes. But, maybe Drop has data indicating that people who buy watches here end up putting their own strap and/or bracelet on the watches they buy.