I view it as more or less irrelevant. LLMs are fundamentally black boxes. Whether you run the black box locally or use it remotely, whether you train it yourself or use a pretrained version, whether you have access to the training set or not, it's completely irrelevant to control. Using an LLM means giving up control and understanding of the process. Whether it's OpenAI or the training data-guided algorithm that controls the process, it's still not you.

Now, running local models instead of using them as a SaaS has a clear purpose: the price of your local model won't suddenly increase ten fold once you start depending on it, like the SaaS models might. Any level of control beyond that is illusory with LLMs.