Fred Grandinetti at Newsarama shares my affection for the original Batwoman and her teenaged, hyphenated Bat-Girl. She's usually dismissed as the "jump the shark" component of Bat-stuff and Bat-people who descended upon Gotham City in the late Fifties and early Sixties. Even Bat-Mite gets more respect.
I always thought it was an attempt to emulate the "Superman family" then coming together in the various Superman titles--which must have worked, since there were so many of them ("family" and titles). Superman headlined "Superman" and "Action", and his younger self Superboy carried "Superboy" and "Adventure". He was also (along with Batman) the lead feature in "World's Finest", and even his supporting cast were getting books of their own, "Superman's Pal Jimmy Olsen" and "Superman's Girl Friend Lois Lane". When Supergirl came along, she shoved Tommy Tomorrow out of "Action" and took over the second story, making "Action" another cover-to-cover Super-title.
But the best Batman could do was for Robin to appear in solo stories in "Star Spangled Comics", before it converted to war stories. Doubtless in some parallel world, there were "Batwoman" and "Bat-Mite" comics, and Tommy Tomorrow shared "Mystery in Space" with the Batman of 2950.
Superman, however, was a Hot Property (fresh from a successful TV series), where Batman was struggling. And editor Jack Schiff was hampered in a way Superman editor Mort Weisinger wasn't: Weisinger could allow his writers to pull a story out of anywhere, due to the fantastic nature of his character. Another survivor of Krypton? Sure. A city of survivors in a glass bottle? Why not? Lex Luthor can synthesize kryptonite? Okay!
But Batman was a human being who dealt with street-level adventures. His stories had to make some kind of sense. You couldn't produce, say, Dick Grayson's parents after all these years (although another set of relatives did eventually turn up). There was a limit to the untold secrets of Thomas Wayne you could pull out of a hat.
Schiff did, eventually, reluctantly, try science-fiction in Batman, and these tales are widely (and unfairly) considered the series' low point.
So, whatta ya gonna do?
Batwoman was, on top of all the other things mentioned in that Newsarama piece, a steady love interest. Batman had never really had a girlfriend strong enough to appeal to both Bruce Wayne and Batman. Batwoman (and Bat-Girl) changed the dynamic of the comic, and I think for the better.
In "Prisoners of Three Worlds", Batman actually told her he loved her.
Unfortunately, that was her finest hour. She had a half-dozen minor appearances more, and then new editor Julius Schwartz turned the comic upside-down, eventually commissioning the creation of another Batgirl.
If DC were to use its new Showcase format to collect all of the Batwoman stories in one volume (they'd fit), I'd stand in line to buy it.