Completely agree. Cloud functions are in many cases a better option than maintaining a server, specially for those background tasks that fire occasionally.
The only issue I've found about using serverless is the database. In most cases (Firebase, Fauna, Cosmos, DynamoDB) you have to couple your stack to the DBaaS provider which is not a great idea. AWS recently announced Amazon Aurora PostgreSQL Serverless but while it allows you to use regular Postgres tools/queries you are again tied to AWS.
One hopes that GraphQL abstractions will enable the decoupling. So if you opt for a database that offers GraphQL natively, it might address the issue. You do have to learn the GraphQL ecosystem (new tools/language etc.)
The only issue I've found about using serverless is the database. In most cases (Firebase, Fauna, Cosmos, DynamoDB) you have to couple your stack to the DBaaS provider which is not a great idea. AWS recently announced Amazon Aurora PostgreSQL Serverless but while it allows you to use regular Postgres tools/queries you are again tied to AWS.