The plan:
Showcase covers follow a standard format of a recoloured version of a cover from one of the comics in the collection. They do not include text on the image. Obviously the ideal image is one that prominently features the title character(s) in iconic pose.
The problem:
All the stories in this collection are either guest spots in another character's comic or backup strips from Detective Comics. The backup character rarely gets cover featured. In fact Batgirl only appears on 6 covers of Detective comics and all but one are where she is appearing in Batman stories. Not only that but there are precious few full page images of Batgirl because space is maximised in her short backup feature and the splash page often contains three panels. On some episodes there is no splash at all, just a title strip at the top of the first page.
So there aren't a whole lot of images to choose from. Let's look at the covers, shall we?














In fact there aren't any covers to comics in this collection that would suit a Showcase cover. But remember this one?

Only problem is that it makes Batgirl look stupid, appearing to be more interested in fixing her makeup than fighting crime.
Of course there are vast numbers of silver age covers that feature the hero behaving in a bizarre or inappropriate way. Batman wore the most ludicrous costumes and Superman was always thinking he was a cowboy or getting a big domed head. So how does it work in the context of the story?
The Story:
In fact the story is all about Batgirl believing that she is too concerned with her looks and making an effort to overcome her perceived fault, ultimately using it to her advantage by distracting the bad guys by showing a little leg, as is pictured on the cover. In fact the examples given of her distraction are first where her mask is knocked out of place and she pauses to straighten it, and secondly where mud is thrown in her face. In both cases her behaviour is quite reasonable as she is in danger of having her vision obscured, so it is possible to read it as Barbara over-reacting to a perceived fault and working to overcome it. This is a bit undermined by her letting out an uncharacteristic scream at seeing Batman in danger; she's never done this before, and it's not even extreme danger, so it's very contrived. But despite this, the story is a positive in that it's all about Batgirl taking control and working to not only overcome her faults but use them to her advantage.
It is a bit cringeworthy, but if you can't accept that women were written clumsily in the 1960's then you won't be reading this volume anyway. Is it better to try to depict a female character having issues different from male characters and do it poorly, or to have no characterisation at all and the only difference between male and female characters is the girl is the one in the skirt, as you'd find in Teen Titans or JLA from a similar period?
In context, the cover depicts a scene where Batgirl is playing on the "silly woman obsessed with her looks" image to defeat the villains, and as such is okay. In a world where the default image of a female hero was the heroic stance associated with a male hero, this would work as the equivalent of Superman in a cowboy hat, or Batman turned into a baby; not iconic, but representative of the fun weirdness of the silver age. But the world is not like that, so it doesn't.
And of course, they didn't use the cover image, they used the splash image. Which does not represent any incident in the story and in fact suggests the complete opposite of the actual theme.

The conclusion:
Yes, it is a bad image to use for the cover of the collection, and one that is liable to put off as many potential readers as if it was all T&A, but given the alternative options, what would you have picked?
Thanks to the Grand Comics Database, from whom I steal many cover scans.