It would have declined and fallen in its 3rd season regardless of who played Batgirl, or whether the show had introduced Batgirl at all.
We don't not know that--all we know is that Craig was the one cast as Batgirl, and her less-than-heroic performance, and not a shred of believability as one who could stand up to villains killed the series. Whatever was poor or retread coming out of season two was no longer a factor, as the dynamic of the series drastically changed with Craig's laughing, stubby joke of a superhero.
Come on, she was slowly delivering high kicks a guy using crutches could avoid, and without being rich (never implied on the show) exactly how did Barbara Gordon build all of her gadgets and that motorcycle, which was ouftitted with more than a few then-high tech devices?
At least with Bruce Wayne & Dick Grayson, the argument could be made that with their millions, they could pay for the elements which made their car, computers, etc., but Barbara Gordon did not have that resource (she was a librarian).
Honestly, I don't think anybody worried about that sort of thing when it came to the old BATMAN tv series. It wasn't supposed to be realistic or plausible.
I can't imagine that anybody actually quit watching because they found Batgirl more unbelievable than, say, the freezing rays and wacky deathtraps. It wasn't that kind of show.
Ten-year-olds back in the 1960s didn't worry about how superheros paid their bills--and most adults saw the show as a campy comedy spoof. Nobody expected it to be plausible or believable.
Getting back OT: "Whom Gods Destroy" is fun and colorful, but undeniably campy. As a kid, I always liked it because of all the cool-looking aliens: An Andorian! A Tellarite! A green girl!
They probably should have cut the whole super-explosive bit, though, as it's just silly and doesn't add anything to the story. An insane, shape-changing supervillain was menace enough without giving him some sort of super-TNT that never really poses much of a threat.