Without delving into the ins and outs of succession planning and mentoring (something that is screwed in 90% of brigades and groups anyhow), lets just look at how things should be operating on the fireground.
You should have defined SOP's that dictate what types of incidents require the Group Duty Officer to turn out. Outside of this, it can be up to them if they wish to turn out, just for the sake of it. We all get bored sometimes. Anyway, once at the incident, the GDO doesn't have to take charge, we need to stop looking at helmet colour and look more at the tabbards that people are wearing. There should only be one person at an incident with the "Incident Controller" tabbard on. What ever colour helmet they may have, they are still the nominated incident controller. Everything starts and finishes with them.
If this is not the case, then its a major breakdown in fireground chain of command, and is very dangerous. There is nothing wrong with 100 red hats turning out to a job, so long as there is only one person who is IC and people, including their peers and seniors, respect the IC position and don't try to throw their $0.02 in.