But removing the cache makes the system slower, it didn't optimize anything. So no, fixing this isn't possible with that approach, you need to take the holistic approach.
There's nothing about identifying and solving one problem at a time that prevents one from taking a holistic approach.
In fact the entire point is to interpret the behavior of the entire system in order to find the right singular intervention. To find the true globally optimal point of intervention, one must look at the entirety of the system.
If you are saying that your method includes all methods, then sure being open to consider all methods of making something faster will include the best way to do it. But I thought were were talking about useful advice here, to be useful you have to narrow it down a bit.