I agree with your take. I made a chrome extension recently (LookupChatGPT) which lets you send selected text to chatgpt using your own custom prompts. I use to think (incorrectly) that System Prompts guide the conversations throughout even after context limit is passed. System prompt just sets the tone for conversation starter. Using my plugin daily, I haven't found much difference either. I can ask questions however I want and ChatGPT will usually just follow.
it is easy to test system prompt and it does make big difference: ask same question “what do you think about china” with system prompt for biden vs trump.
I am not saying it doesn't make. It does set the tone/context of next responses. But it's not a permanent guide throughout the conversation, it can be changed to do whatever you want in your next messages.
of course. in my case, i am using this list for telegram bot. Bot users have no clue about system prompts - and it looks like magic to them when you switch to new "assistant".