Fact: If ice were perfectly smooth it would have nearly zero friction. Say you were stuck in the middle of a of body of perfectly smooth ice. With zero friction you can't walk to the side, your feet can't find a purchase, you cant even stand up! How do you get to the side?
I live on a severe incline. Over the years in winter I've been within sight of the door and unable to ascend wearing my docksiders. I take them off and get traction with my barefeet so I don't end up in a scene from Dr Zhivago. So, I must disagree.
Talking to the ice in a calm, persuasive voice while perambulating on and around it can help. Fact. Adopting the Cockney accent Dick van Dyke employed in Mary Poppins while you do so will aide your passage even more (but don't try any of his hoofing manoeuvres!).