I ran across an Instagram post the other day which was a split screen of a model's feet. On one half, the model was wearing what looked to be 4 inch stiletto sandals. On the other half, the model was wearing 4 inch block heels with a mild platform, less than an inch. The caption read something to the effect of, "Which one is more likely to cause you to sprain your ankle?"
I have yet to answer one of these kinds of things, even though I want to. I didn't reply to this for two reasons: 1) I was on my phone, and didn't feel like typing out a long reply, which is what it would take. 2) The post was already 3 weeks old, and had probably 500+ replies. I don't need to waste my time for that.
My answer, of course, would be, "It depends." For most situations I am in, however, the single sole stiletto is more my friend, though I can't say that I'm worried about spraining my ankle in any case. I wear platforms all the time out in the wild, and it's absolutely true that if you step on a pebble or a twig in platforms, it's going to apply a lot of unwelcome sideways force to the ankle, a force that would be much less in single soles, regardless of heel configuration.