I was working on writing a script to list the app pool for each service application and I got to the State Service and Usage and Health and Data Collection Service and don't see any app pool property for the object.
There is no App Pool associated with the State Services, because it is just a container(maintains state for user sessions and many out of the box features). What I am thinking, whoever (I mean services application or web application) want to use this state services, use his own app pool & sharepoint services for it.
There is no App Pool associated with the "Usage and health data collection". Again, SharePoint uses timer jobs/ services/ SQL procedures to move the data from logs to database.