You've always been free to serve your static assets in any way you like, so I'm unclear as to how the way the backend is architected comes into play here.
Though I tend to agree I'm yet to hear a really compelling description of why I should move very much into it. Some of this may be because I tend to write in a style that makes it fairly easy to mix & match bundles of application functionality anyhow, so to me adding some tiny function to a running app isn't that big a deal. (I don't use Erlang directly, but Erlang is where I learned this from.) If you're in an environment where deploying a single new REST handler or some recurring service is much harder, though, I could see where it comes in handy for certain things.
Still, not sure how damage control for poor performance is a "pro" of serverless design.
I just want to quickly deploy code in a friction and maintenance free manner with zero compromises on scalability, latency, flexibility or reliability, what the problem is?