I had never thought about this but you're right. Big frozen water/soda bottles of ice still increase the overall thermal mass and will almost certainly slow full thawing. Otherwise, ice blocks in a cooler wouldn't work.
But you're really better off adding salt to those bottles so they absorb energy when melting below the freezing point of pure water (and frozen food).
While that's true, since the current topic of this conversation is about emergency preparedness, I think having potable water (in ice form) would be much preferable to salted water.
It’s substantially more efficient to store a pack of bottled water or two on top of your fridge - and keep your food at the same time. Water keeps well even if not frozen.
If you want to keep tap water, you can buy silver ion additives at any camping/outdoor store. If you’re really planning for preparedness, buy a ceramic water micro filter and additives. That can make nearly all water usable.
But you're really better off adding salt to those bottles so they absorb energy when melting below the freezing point of pure water (and frozen food).