A realization here is that while reaching cold start times that allow for individual requests would be awesome, you don't need to reach that to benefit from attacking the cold start time:

Every millisecond you shave off means you can afford to run closer to max capacity before scaling up while maintaining whatever you see as the acceptable level of risk that users will sometimes wait.

Of course if the customer stack is slow to start, the lower bound you can get to might still be awful, but you can only address the part of the stack you control.