Would you agree that raising your hand, aka volunteering to do more work, is the universal success tactic? It definitely shows initiative and leadership.
However, there are levels to this skill.
Level 1: The boss says, “I need someone to take on X project.” You say, “On it, Boss”. And now you have a new responsibility
Level 2: You ask your boss, “Is there anything I can take off your plate?” The Boss will usually decline this offer, even if the only reason is the boss is too overwhelmed to think about what s/he could offload to you.
Still, it’s good to offer help in this way. If you keep asking, you will eventually enjoy a new responsibility.
Level 3: You say something like this to your boss: “Hey! I noticed that you’re still dealing with X task. How about if I take care of that for you?”
The Boss will think that s/he is hallucinating, or hearing angel voices. S/he may ask you to repeat what you just said. And probably, you will have a new responsibility and a very happy Boss.
The thing is, before you can take on NEW responsibilities, you have to deal with what is on your plate at the moment. It’s not always a good time to take on something new.
Even so, those who raise their hands more often are those who rise to the top. Teach this to your team and watch the ensuing transformation.