The status quo is if you don’t moderate for a month somebody can challenge you as moderator and take over. People who took over communities in this way, and now cannot be displaced because of their activity, literally are moderators because they did something voluntarily.
That’s just on the admin level, mod to mod, generally users who are active and willing to do the work are more likely to be promoted to mod and less likely to be kicked from the mods.
But in short, yes your willingness to do unpaid labor is absolutely part of what entitles you to be a mod. It’s not always sufficient but it’s often required.