Heat transfer of big ice cubes

So big ice cubes aren’t necessarily new news, but the ad below which piqued my interest is recent.

Ice is cold; your drink is warm. If ice cools drinks by taking heat and melting, then can these work as advertised? The larger surface area slows melting and heat transfer, true, but no heat transfer means no cooling! So you could put big ice cubes in your drink and they wouldn’t make it cooler in the same way. Right? 

Or, if your drink is already very cold, maybe it helps a bit more, but I keep seeing calories (i.e., heat energy) go into your drink – from the sun or simply ambient air temperature. Ice can suck up lots of those calories because its heat of fusion (about 80 cal/g) is so much higher than its specific heat (1 cal/g). BUT again, if the heat transfer into the ice is slowed because of lower surface area, then the heat has to stay in your drink, right?

Maybe they just make better decorations by not melting, which is a whole different problem.

It seems to me that the polished stones you can pop in the freezer are a better choice – infinitely recyclable and high thermal mass. As long as you don’t chip a tooth trying to chew on them!