It doesn't but it will have latency when loading in the KV keys for every non-cached request.

Don't KV loads not count towards the CPU time of the request?

Loading a KV does not take CPU time, however, loading a KV into a variable does parse the content of the KV which does consume CPU time.

Which is why it takes a lot less CPU time to do streaming and even to some degree, a streaming parsing of the content.