I can see that maybe there is a case to make for using functions as a service, to handle batch processing of things, or possibly to service background API requests.
2. Cloud vendors are working and succeeding to make cold starts faster, and AWS is at the forefront.
3. Pre-warming done right is extremely cheap, you won't pay anything meaningful, just several cents per month.
P.S. I'm the author of OP.
This is called "predictive autoscaling". In other fields it's called seasonality and you can build inventory and manufacturing plans around it.
While researching FaaSes last year I saw a slide deck from an Amazon PM about Lambda (I promptly lost the link). The thing that stuck with me was a claim that a substantial amount of their autoscaling "magic" was due to predictive autoscaling.
Netflix wrote up[1][2], but have not opensourced, their predictive autoscaler "Scryer" in a few blog posts. The tl;dr is that they use a combination of fourier transforms and simple correlations to make a basic forecast of how many VMs to have ready at different times of day. A reactive autoscaler adjusts on the day.
[1] https://medium.com/netflix-techblog/scryer-netflixs-predicti...
[2] https://medium.com/netflix-techblog/scryer-netflixs-predicti...