Sysadmin

I don't know what you're referring to. Most serverless requires docker, like Fargate ECS. You can even run docker in lambda now.

It's literally the convenience of not having to manage the hardware and pay per use, rather than always on hardware.

Same with serverless PaaS options like Aurora, Dynamo, Rekognition, etc.

That's worth a lot to a lot of people in the industry. Sure, you can save more money by running it on hardware you reserve and maintain, but that's the cost/benefit analysis you need to make on a case by case basis.