Freezing water releases quite a bit of heat (or, if you prefer, “takes quite a bit of cold”). In fact, the amount of energy required to melt ice is almost the same as the amount required to raise it from freezing to boiling once it has melted.
The ice just isn’t cold enough. A very cold freezer has ice at maybe -10 C, meaning you’d need an ice-to-water ratio of 10:1 or so for the warming of the ice to cool the water down enough to freeze.
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