From a 2007 paper by Josiah Ober at Stanford titled “What the Ancient Greeks Can Tell Us About Democracy” (PDF)…
She explains the Assembly’s annual decision of whether to hold an ostracism, and the occasional (only 15 recorded instances) of actual ostracisms, as a repeated ritual through which the mass of ordinary Athenian citizens reminded Athenian elites of the power of the people to intervene in inter-elite conflicts if and when those conflicts threatened the stability of the polis. Forsdyke argues that the Athenian revolution itself, and thus the origin of democracy, is best understood as a mass intervention in what was formerly a exclusively elite field of political competition – and that the signal success of Athenian democracy was in the regime stabilization that emerged with the credible threat of mass intervention.
Recalls and impeachments don’t do the job of intervening (like ostracisms) in what has become a very exclusive process of government in the USA.