Except now you don't need an infrastructure team. That's the whole point of serverless architecture: to be able to scale without having huge team scale as well.
You haven’t needed an infrastructure team since PHP shared hosting, and certainly not since Heroku or Elastic Beanstalk, except that people kept wanting greater complexity at lower cost. There is nothing new about “serverless” there.
There is a difference between what was then and what is today. The key difference is that the "serverless" term is massively overloaded here and once you dissect it you will see that it's a mix of multiple serverlessly managed services that we are able to take advantage of: Kinesis, DynamoDB streams, Kinesis Firehose, SNS, Lambda, Cloudwatch, and GraphQL/AppSync. Serverless computing came a long way.
Agree that serverless is a buzzword here, just as data science and machine learning have now become. It is about taming greater complexity at lower cost, and at increasingly more granular levels.