I use lambda to perform simple, stateless units of work like autoscaling event post-hooks, chat bots, routine scheduled tasks, etc. They're mostly cloud-agnostic and I could move them to a server if I had to.
I don't think anyone can really build a full scale application using serverless. It's just not performant or predictable enough. I've seen people try, and it always ended in frustration. A properly configured docker scheduler is better for this type of work anyway.
You can definitely build a fully functional web app using just serverless. For an example, take a look at https://acloud.guru . Where I work, we almost exclusively use serverless, and I have found it to be incredibly reliable, and way more hands-off than a docker deployment.
I don't think anyone can really build a full scale application using serverless. It's just not performant or predictable enough. I've seen people try, and it always ended in frustration. A properly configured docker scheduler is better for this type of work anyway.