I'm a senior dev, and generally reserved. I will make a suggestion once if I think it's worth pursuing, but never again. Louder devs get their way over me often. I don't mind. It's exhausting defending your reasoning to people who want to shout theirs instead of reason things out calmly and quietly together.
If you're happy with his "good player"ness, then leave him the hell alone. People trying to crack me out of my shell "because reasons" get an opposing and forceful response from me. I hate feeling manipulated against my will, and if you want me to be some sort of performative marionette and not a coder, then we're not right for each other, and I will be leaving soon.
Weigh where you value this developer. Not everyone gives a hang about "contributing to the company's progress" in the macro, and are content with micro problems.
I say this as a Sr. who has been somehow railroaded into a Lead/Management role that I loathe, and it has ruined a great situation for me, and it will soon ruin it for my employer. And my manager doesn't understand my objections, as many times as I have told him.
$0.02. Have you bothered to ask this dev if his quietness is indicative of anything other than his shyness and reservedness that you already knew and are somehow not respecting? Maybe Email it and await his response. It might blow your hair back. The howler you'd get from me, if I respected you enough to be honest, would certainly adjust your posture. :)