Yes, and no they aren’t, you’re probably just thinking of icy conditions, where there is ice, snow, salt, bare asphalt, etc. They’re great for that.
But I’ve driven across a frozen Lake Erie with no snow (we used do that sometimes to get to the islands when the ice is thick enough) and it’s just pure ice. Nothing but chains makes much difference then.
But outside of rare stuff like that you’re not often on just ice, so OPs comment, while I agree with it in fact, it’s kind of an “aaaaaactually”.
Ah, literal ice - well, certainly that is out of the normal use for the tires? Snow tires definitely help for "road ice" or "snow that has become ice" - I had to once drive up a fairly steep driveway of "snow that was now ice" (where you could not walk up it without crampons) and my snow tires did a great job with my AWD - I was extremely impressed.