The Naboo Queen seems anything but a figurehead. For one thing, they couldn't force a settlement without her. We saw her command troops into battle, speak on behalf of her world in the Galactic Senate, forge an alliance with an until then belligerent neighbour, and had enough sway over her security detail that they let her tag along with a Jedi on a Hutt controlled outer rim cess pit of a spaceport.
The remarkable thing is what it says about the state of the educational systems in the Star Wars galaxy when it's even possible for a human to be considered fit for high office while still a teen. Not just Padme, but Leia was also a teenager when she took over as Senator, and I'm pretty sure Senator Chuchi is meant to be not too far off Ahsoka's age in TCW (though it's hard to be sure.) I think Lucas said at some point that Leia had the equivalent of a PHD before she was a Senator.
For those hung up on the idea of voting for a Queen; believe it or not elective monarchies are indeed a thing. They usually end up becoming hereditary ones, which may or may not have happened with the Naboo at some point in the past. Or maybe they've gotten lucky and have been electing their Queens since they settled there.