(I work at Stripe.)
We've thought about closing HTTP access in the past. As with a lot of security, it's a usability trade-off.
We work hard to make sure that people only ever access Stripe over HTTPS. Most people use the Stripe API through an existing library. Since the API doesn't work over HTTP, any such library is guaranteed to use HTTPS. Stripe itself is on Chrome's built-in HSTS list, sets HSTS headers, etc.
The scenario Stevie describes is unlikely to be an issue unless the user is implementing his or her own library. In that case, though, they're almost certainly going to be using test API credentials. Stripe's API will never return a successful response when you access it over HTTP, so you'll figure out that you can't do this on the very first request.
More broadly, what exactly is being defended against isn't particularly clear. There are much easier ways for someone implementing their own library to screw up (skipping cert verification is extremely common and leaves you perpetually vulnerable to HTTPS MITM), and there are many other plausible vectors for an attacker.
Even if we did change this, we'd only have solved one small class of accidental key leaks. You could accidentally specify "stripe.com" instead of "api.stripe.com", for example, and stripe.com will of course always accept HTTP. Or you could typo the domain and send your key to someone else entirely.
If we ever did want to solve this, we'd probably do something like:
- Monitor HTTP Authorization headers sent to api.stripe.com.
- Notify the user if they ever accidentally send a secret key in the clear.
- In addition to notifying the user, we could potentially roll the key automatically (though this runs the risk of breaking production code).
But I don't think disabling HTTP helps much. (I do think it'd be good if we started monitoring the frequency with which this happens -- if it's common, we should certainly do something like the above; if it ~never happens, it presumably doesn't matter.)
Separately, I think that the HMAC-based signature scheme that Stevie proposes is something we might want to do at some stage. A very early version of Stripe actually had something very similar. The issue with all protocols in this vein is that they involve considerably more complexity on the user's end and are harder to debug. But they definitely have some nice security properties.