Uh, you can definitely implement a standard CRUD app with one of the serverless platforms. You can even throw an entire expressjs application into a lambda function with minimal modification if you want.
using lambda and its equivalent is - in my understanding - the definition of serverless. You might not be able to utilize the biggest advantages of serverless infrastructure if you combine it with a standard ACID database backend, but it should still be a serverless deployment.
This is the first general misconception with serverless.
Serverless is not lambda . If you think serverless == lambda, it's like saying cloud == ec2 . You're missing the point of it.