In real life, successfully fighting societally recognized enemies gets you all kinds of political opportunity.

Well, yeah, it got Quirrel's "hero" political opportunity too. He was invited back to the fold of the Most Ancient House, and after the death of everyone else there, he would have wielded the vote in the Wizengamot. But they didn't sufficiently obey him as leader.

Look at American Presidents Eisenhower, Grant, Taylor, Jackson, Harrison, and Washington.

Alcibiades was accused and recalled by the Atheneans while on the expedition he had been advocating. Pausanias (victor of Plataies) and Miltiades (victor of Marathon) barely lasted a year after their famous victories, before getting accused of treason.

But within the context of the story, Quirrell's "I fought the villain but got no respect" is nonsense. Humans don't work that way

Knowing something of Ancient Greek history, and how they tended to treat all their most successful generals, it seemed very believable to me.