Cass and her amazing changing boots!

Over the course of Cass' comic book career artists interpreted her costume differently, including her footwear. Damion Scott favored drawing Cass in sensible flats, for example.  Think about Cass and her hit-first-don't-ask-questions-later-or-ever approach to life and crime fighting.  More than likely she'd choose footwear that gives her a combat edge.  Some sort of specially-designed sole allowing her foot ample support and traction as she runs, jumps and kicks all over Gotham City. 

And still, we find Cass taking on a whole bar-full of muscle goons while wearing the chunky disco heels artists N. Steven Harris and John Nyberg give her in Birds of Prey #27 (March 2001).

Disco, or else she broke into Gene Simmons' dressing room.  Admittedly, chunky disco heels permit sweet post-fight interrogation moves like this:

But since Cass was never really one for interrogation, I can't see chunky disco heels as anything more than a male artist's idea of female fashion affectation or an attempt to introduce an element of BDSM into Cass' look, which, admittedly, tends to skew that way when an art team renders her costume as leather or shiny plastic.  They're more robust than traditional heels, though.  Your more traditional heels can cause embarrassing incidents like this, from Batgirl #45 (December 2003), as visualized by Rick Leonardi and Jesse Delperdang:

I think it's much more likely Cass would have snapped one of those more slender heels with her fighting moves than this "slipping on them" business.  That's just silly.  High heels or not, you have to imagine Cass always aware in some way of her center of gravity and subconsciously making adjustments.  With these comics coming roughly two years apart, we can assume the relatively more stable platform the chunky disco heel provide gave her over-confidence concerning Barbara Gordon's old boots.

But that still doesn't explain why she changes boots partway through that Birds of Prey issue.

Flats!  They're not even the same color!