Chromeless looks promising. Being able to run a load of scrapers in parallel at certain times could be useful if time sensitivity is an issue. E.g someone sends you a batch of URLs to screenshot and each site takes a while to render. You could use lambdas to run all those processes in parallel instead of wasting money keeping capacity lying around just for those spikes.
I suspect it makes economic sense only when your workload is relatively elastic, having a relatively low duty cycle. The ability to pay less when you aren't actually using any resources is likely of more economic benefit as it becomes more fine-grained. If you aren't in that position, other models of lease or ownership of computing resources probably merit consideration.
Well, to be honest I pay 40€/month for a baremetal server (i7 SkyLake, 64 GB RAM, 4TB HDD). It's a powerful machine running many services, including a few virtual machines. I consider whatever it does would qualify as low-duty. Now, I know that each month I'm paying 40€ for all this. The last time about I read about serverless was when someone directly discovered the money saving part is quite tricky: https://news.ycombinator.com/item?id=14982220.
That's a general answer on how you can save by using the cloud, I specifically meant the "serverless" variant.
(Apart from that, I think this is a misconception - Amazon seems to have convinced people you don't need a sysadmin anymore, whereas in fact once you start exploring the whole AWS infrastructure and its complexity, you quickly realize you still need sysadmin's knowledge plus understanding of how their services work and all their quirks.)
I understand that with AWS, you need a sysadmin. That is why I was saying with serverless (in this case, AWS Lambda) you didn't need a sysadmin. I assume it's the same with Google Functions and whatever Azure has.
But you will need other things... you need some kind of fronting system to tie things together, you need some sort of DB/Storage. And while you can get away with fewer admins, someone will be spending part of their time in a sysadmin role. It's more a matter of how much can get done with how many admins.
I get the point you are trying to make, but as AWS offers many services, I don't need a sysadmin for a DB (RDS, Dynamodb, ElasticSearch, S3) or for APIGateway nor for any coordination between systems (SNS, SES)
True serverless let's me offload that cost to AWS instead of having a sysadmin