sub 10 ms would only work if they had an instance running and warm, ready to take requests - if they still have to look up your function, provision a machine, interpret it etc it's easy to go past that. 600ms is still respectable if it's from a "cold start".
But if you've got time critical applications maybe serverless is not for you.
I know it's an edge case that doesn't fit Amazon Lambdas atm. I do it by hand ATM, so I know it can be done, but sure I run it on too many preowned servers to handle peaks. Controlling serverless resources in a more fine grained way is a way to use your servers more effectively.
But if you've got time critical applications maybe serverless is not for you.