For another, the dependence on a random seed is just one example of how you can get different behavior. You could just as well get different results due to e.g. a tiny difference in prompt wording or punctuation or whitespace.
If a model passes some test on 70% of random seeds, and fails on the other 30%, then knowing the rough probability of success is much more useful than knowing one random sample of the outcome.
And empirically this kind of probabilistic success is quite common, because many LLM benchmarks report "pass@k" success rates that are much higher than the "pass@1" success rate on a single attempt.
Tiny variations in the computational environment, such as slightly different set of processes running on the system as well as tiny differences in core temperature or voltage - among many other factors, can cause computations to complete in non deterministic order relative to each other.
This meaning one run eventually calculates a+b+c, whereas another does a+c+b, yielding slightly different results. Those cascade down the chain, resulting, finally, in a different set of produced logits.
Notably, similar effects can and do affect pure CPU calculations on multi core machines, and as a matter of fact even on a single core depending on the architecture when considering eg pipelining, branch prediction etc.
Thus, real world matrix operations are not, in fact, deterministic.
Now, one could argue that all of these are negligible, but that is an empirical claim dependent on the problem at hand.