Reasoning improves the output of the model. Originally it was a prompting method called chain of thought but later models were trained to do the reasoning steps without the human prompting for it. Being able to see the reasoning steps is just an accidental benefit.
Even if it is intelligible, reasoning styles (and hence reasoning effectiveness) differ between models.
For example, gpt-oss loves reasoning in the style of "I be caveman, hungry, need food, need coconut, will search coconut now, eat when find." Giving that to a model unaccustomed to that style could cause it to respond like that.
Reasoning interpretability helps debug why models fail (and some labs will give it to you if they trust you not to distill or be hacked), but there are also conflicting goals like token-efficiency, so interpretable reasoning doesn't always mean "pretty sentences".
https://arxiv.org/abs/2201.11903