In general, serverless computing tasks cost 100-1000× more per cpu cycle than a counterpart running on a cloud server.
That means that for tasks that are running regularly, they are a huge loser.
They have unpredictable latency, you lose control of things like logging to disk (you get locked in to cloudwatch or whatever, yet more money and tooling required)
The notion of scale seems promising at first, but I would be very skeptical before I accepted the claim that someone can scale lambda volume from 10 to 10 thousand executions per minute without setting off alarms, dropping traffic, and probably having an engineer at AWS Lamba get paged.
So what are lambdas good for? I'd argue that they make good glue for deployments or batch processes that happen infrequently, don't require predictable performance, and for which having a dedicated server is a little wasteful. I'm skeptical even of those. Remember, a micro server is free tier.
I have had success building prototypes with AWS Lambda, so there's that aspect too.
I'd be interested to hear a counterpoint from someone who uses serverless compute in a large enterprise setting in place of a traditional server stack.