They want to have a rapid response path (little to no delay using staging envs) to respond to emergencies. The old SOP allowed all releases to use the emergency path. By not using it in the SOP anymore, I'd be concerned that it would break silently from some other refactor or change.
Your notion is to maintain the emergency rollout as a relaxation of the new SOP such that the time in staging is reduced to almost nothing. That sounds like a good idea since it avoids maintaining two processes and having greater risk of breakage. So, same logic but using different thresholds versus two independent processes.