This isn't how it works. As the developer, you use the system prompt to set a particular personality for the chat bot. Eg, when you use an LLM in VSCode, it comes with a system prompt to make it an effective code assistant.
Now, in VSCode, you can select a different model, which is maybe where your misconception comes from. But when you select a different model, it will also use a different system prompt, designed to achieve the same personality, but tailored for that particular model.
Once you figure out why they do that, you'll understand why your position here doesn't make sense.