You probably need a couple GB to cache a conversation. That's not so easy at the moment because you have to transfer that data to and from the GPUs and store the data somewhere.
You'll notice in their video [1] that they never show the prompts running interactively. This is for a roughly 800K context. They claim that "the model took around 60s to respond to each of these prompts".
This is not really usable as an interactive experience. I don't want to wait 1 minute for an answer each time I have a question.
If you are going to ask "then why don't OpenAI do it now", the answer is it takes a lot of storage (and IO) so it may not be worth it for shorter context, it adds significant complexity to the entire serving stack, and is incoherent with how OpenAI originally imagined where the "custom-ish" LLM serving game is going to - they bet on finetuning and dedicated instances, instead of long context.
The tradeoff can be reflected in the API and pricing, LLM APIs don't have to be like OpenAI's. What if you have an endpoint to generate a "cache" of your context (or really, a prefix of your prompt), billed as usual per token, then you can use your prompt prefix for a fixed price no matter how long it is?