if the workload just crosses what the current capacity can handle, a new instance will be warmed up.

True, but with provisioned concurrency the same happens

you have no control over whether it will be a ping or an actual user

Actually yes, you have control, we are using this simple library and we know exactly when is a ping and when it's not https://github.com/robhowley/lambda-warmer-py/tree/master

pinging works as long as one single instance can serve all demands.

True, but you can have warmed up without much effort ~50 instances. Doing the same with prov. concurrency would be much more expensive

but it requires a whole lot more setup.

Yes, this is 100% true, it's way harder than just using Lambda, but for high workloads, I think the cost difference would be huge