Very interesting discussion. 
Following automakers DO NOT recommend Engine or Transmission flush:
- GM
- Chrysler
- Ford
- Nissan
- Volvo
- Honda
- Mitsubishi
This information is obtained directly from these automakers. You are welcome to call them directly or send them an email to confirm it. 
When I contacted Toyota, they didn't have an official recommendation but their dealer maintenance facilities will not perform these procedures.
The reason for why not is that there are very narrow channels and one-way valves in modern engines and transmissions that may get blocked if a solvent of any kind is used to dislodge large particles during flushing procedure.