Exactly, it's because we don't have an ice maker, and regular ice containers make ice that tastes like ass. I think we got them a long time ago at Dollarama.
Last ice bags I saw have cube shapes with little gaps between them to allow the water to fill the bag. So when you rip the bag open they're already more or less seperated.
As for the taste stuff, not so much the ice container, but if it's not fully sealed it can take on the smell and taste of other things in the freezer.