A bit of nitpicking, a temperature of zero does not really exist (it would lead to division by zero in softmax). It's sampling (and non-deterministic compute kernels) that makes token prediction non-deterministic. You could simply fix it (assuming deterministic kernels) by using greedy decoding (argmax with a stable sort in the case of ties).

As temperatures approach zero, the probability of the most likely token approaches one (assuming no ties). So my guess is that LLM inference providers started using temperature=0 to disable sampling because people would try to approximate greedy decoding by using teensy temperatures.