CGI is also the way the web used to work. Spawning processes has only gotten faster since then. The entire "process spawning doesn't scale to the modern web" argument is completely and totally bogus. Today, spawning a process in Linux is only 10-20 microseconds slower than creating a thread: http://www.bitsnbites.eu/benchmarking-os-primitives/
The performance problems are elsewhere.
The folks who started at a small scale in serverless but see traffic growing and kind of are in the middle space before jumping to dedicated servers have an entire art form of keeping their functions "hot" since both Lambda and AppEngine actually keep your functions hot loaded when once it's spun up for some time.
https://www.google.com.sg/search?q=serverless+warm+up&oq=ser...