I was hosting my personal website on EC2 with an RDS instance and it cost around $20/month. But since the site gets little-to-no traffic and I got sick of EC2 upkeep, I switched S3 & Cloudfront: now my bill is $0.80/month.
Another example: at work we inherited an old EC2 instance that was set up solely to run cron jobs on other servers. Occasionally it would lock up or go down, for whatever reason, creating chaos for the servers that needed specific jobs run frequently.
We switched to AWS Lambda functions for those cron jobs and they've never failed once.
If you're running a games website that gets pinged 24/7, don't use Serverless. But the notion that it's slow and overpriced is misguided if you're applying the wrong use case.