> Public servants normally can be fired by elected officials.
No, they can't. There are extensive laws, rules, and regulations that prevent elected officials from firing government employees arbitrarily.
> Elected officials can be "fired" by the people, albeit only once every 4 years.
Every 2 years for the House of Representatives, every 6 years for Senators. But that almost never happens; the US Congress has incumbent re-election rates well above 90 percent. US Presidents are limited to two terms, so every so often we are forced to choose a new one.
Perhaps spun into some sort of not-for-profit, like Firefox. It's a difficult problem. Most options seem bad, but the current situation is bad too.