Summary
If an instance has many remote agents with many capabilties,
com.atlassian.bamboo.plan.ExecutableAgentsHelperImpl.getExecutableAgents is slow to determine which agents can run plans/jobs/stages. This has an impact on the plan configuration UI when you try to modify stages, which causes this part to have long loading times.
This is exacerbated if the underlying database has performance issues of sorts.
Workaround
Under certain circumstances increasing numHelperThreads in bamboo.cfg.xml may improve performance.