Your suggested functionality is server side, not client side.
> it uses API's unused capacity
I see no waiting or scheduling on my usage - it runs, what appears to be, full speed till I hit my 4 hour / 7 day limit and then it stops.
Claude code is cheap (via a subscription) because it is burning piles of investor cash, while making a bit back on API / pay per token users.
Why would scheduling be a thing in this case? I might be missing something here.
With continuous batching, you don't wait for entire previous batch to finish. The request goes in as one finishes. Hence the wait time is negligible.