The scaling of serverless functions is a pretty major point of difference between them and SFTPing a PHP script to a shared web host. Another difference is isolation of your code from anyone else's code; this can vary widely between shared host vendors but with serverless functions you don't "neighbors" to worry about, in terms of server load or security (their code being exploited or your code being exploited).

Serverless functions seems like a nice addition to sites that are 98% static but need a little server-side code specific to the task.