This neatly cleaves responsibility: your business logic team can just build+deploy+expose functions; and your frontend and ecosystem teams can build+deploy+expose the APIs they want on top, perhaps being maintained within their own codebases.
These can even be done on two entirely-separate platforms, rather than both being a part of the same “serverless” IaaS. You could use any combination of commodity FaaS providers (including your own hosted FaaS clusters) to deploy functions to; and then you could use some “smart” load-balancing system (e.g. Cloudflare Workers, or the routing component of an FaaS) to do the routing+aggregation on.
What I've seen AWS Lambda being used: One-off functions with manual output management. They aren't really being chained together.
Can you elaborate? It sounds like you're saying that if you write code that's deployed to a serverless infra you end up with 'serverless code'. This hasn't been my (very limited) experience - where the serverless stuff is just a thin layer around your business logic.