The explanation is in the article. Tldr is for sync functions, the CPU is blocked, with async functions, once the await statement is reached, other stuff can be handled in between
To restate my comment: I argued (1) this CPU cost would be very marginal compared to the LLM API compute cost, and (2) the CPU blocking claim doesn't really hold, due to the wonders of threads and processes.
1. A blocking call, which can take 3-10 seconds.
2. A streaming call, which can also take 3-10 seconds but where the content is streaming directly to you as it is generated (and you may be proxying it through to your user).
In both cases you risk blocking a thread or process for several seconds. That's the problem asyncio solves for you - it means you could have hundreds (or even thousands) of users all waiting for the response to that LLM call without needing hundreds or thousands of blocked threads/processes.
Or maybe the disconnect is where I'm taking for granted that "cost of parked thread" is the same as worrying about the nr of parked threads? Maybe everyone uses Django setups where it's nontrivial to add memory, increase serverless platform limits, etc if you get the happy problem of 10k concurrent users? Or maybe people don't know that the nr of threads/processes you can have on Linux is much more than hundreds or thousands. Or maybe there's some Python or Django specific limits to this.
See eg https://www.baeldung.com/linux/max-threads-per-process for some runtime sysctl knobs if you want to go higher than the default limits. (Though the section 6 there seems out of date and written with the 32-bit OS in mind)
[1] as reported by the Python snippet from https://stackoverflow.com/a/64406494