There are numerous reasons why a developer would want to have their root_agent not be an LlmAgent, and to instead have a coordinator LlmAgent somewhere a bit deeper in the agent tree that then controls a bunch of sub_agents. Yet in these configurations it's not possible to use global_instruction, even though it would be a very useful feature.

global_instruction should instead apply the agent it is defined on and their descendent agents down the entire tree. Multiple global_instructions on a tree branch should be concatenated. It should also probably be defined on BaseAgent so there would be no limit on how it can be used in an agent tree. Non-LLM agents would simply ignore it but could still pass it on to their descendants.

Perhaps "global" would no longer be an appropriate name for this, but such an implementation would be much more useful and flexible than the current one.