I've always ordered soft drinks at restaurants without ice, too. It's because, if you don't, half your drink will be ice, and then it will melt and water down your drink, so you feel the need to drink it super fast before that happens, and then you don't get to savor the drink and you just end up with a brain freeze.
It never really bothered me to ask; to me, it's like asking for a burger without tomatoes or something (because tomatoes are awful). But I do have it sometimes where, when I get to the counter or whatever to place my order, my brain locks up or whatever it usually does when I'm put on the spot, and I completely forget to ask for no ice. And then I have a drink that's half Sunkist and half water.