"Ah, the pitter patter of tiny feet in huge combat boots.”
Captain Mal Reynolds, ‘War Stories’
Zoe wears tall brown leather boots with a flat heel. Kaylee sports comfy shoes that look a little like modified hiking boots. River has combat boots, or she goes barefoot. Even the Companion, the most elegantly dressed of all them, doesn’t glide across the ship in heels. Heels would get stuck on the floor grating. We don’t see Inara’s footwear a lot, but they appear to be sensible slippers or occasionally sandals. Sturdy enough to handle ship life and easy to slip on and off for work. I would think that’s an important consideration. Dealing with laces in that line of work could be bothersome.
It seems like a small detail to consider when you're planning out a television series. But I don't think I would have admired Zoe as much if she ran around shooting her rifle in 4" chunky heels. There's a credibility factor. I can suspend disbelief for most things in science fiction, but impractical footwear? That sends me running (cause I'm wearing comfy boots and I can)!
All this comes from a person who rarely wears heels. They’re painful, and also – I’m clumsy. Heels end in blisters or embarrassing falls followed by colorful bruises. Even if I were entirely comfortable in them, I couldn’t imagine wearing them if I were say, a doctor on the U.S.S. Enterprise. Sure, the floors are covered in industrial carpet. It’s safe from that perspective. But you never know when the red alert will sound. Platforms do not scream ready-for-action.
I’ll take Big Damn Hero boots any day.
Note: I exaggerate to make a point. Sensible shoes are also common throughout SG-1, most of Star Trek, Farscape, and many other shows.