Eichmann wasn't just some bureaucrat but wanted to be seen as just a cog in the system. She basically ate his act and now everyone has to bring her up whenever something evil happens which people seemingly don't seem to care about. In reality Eichmann was a man who had genuine ideology, was personally driven and extremely calculated.
Raul Hilberg holocaust expert is a better source for information on Eichmann, he wrote (one of) the best works on the holocaust and is a genuine historian, was one of the first people to write an extensive history of it . He's not exactly as promoted today (in the media/general public) as actually following his view would poke some holes in the 'holocaust industry' (this doesn't mean that I in any way minimize or doubt the holocaust and its cruelty).
When you're looking to get laid you don't ask a lot of questions about politics. Same goes when you're looking for a job. Soon enough, you -- or your offspring -- are part of the machine. And that's the banality of evil.
But moreover, Heidegger didn't just "turn brown". He saw NAZIism as a potential realization of his philosophy. Such a belief definitely influences my view of Heidegger. Any summary of Heidegger's philosophy and it's problem naturally either involves a lot of simplification or is book length. For book length critiques, I'd recommend The Jagon Of Authenticity by Adorno. My simplification of Heidegger's weakness is that he among a number of philosophers criticizing the lacking of authenticity/awareness/true-being/etc in the modern world in isolation. Such critiques tend to fall for political movements promising the violent reconstruction of tradition - such as NAZIism but limited to that. Michelle Foucault's despicable endorsement of Ayatollah Khomeini on the eve of the overthrow of the Shah is quite similar Heidegger's turn.
The point is that even someone as brilliant as Heidegger could be captured by insane ideology.
You are obviously also captured by an ideology,if you can see it or not.
And the idea that Hannah Arendt needs "defenders" because she had an affair with Heidegger is just bizarre.
Heidegger aimed to use the NAZI movement to promote his own ideology, which he viewed as compatible with and appropriate to the movement. It was different from other versions of NAZIism and they were different from each - only at point the NAZIs fully consolidated their state control and wielded top-down state propaganda did things become uniform. But the idea-point leading up to that point (say, about when Heidegger resigned his rectorship, after The Night Long Knives) should most simply and clearly be called "NAZI ideologues".
And yes, that's not something those who like Heidegger's writings like to hear.
I gotta mention that Arendt relationship with actual NAZI ideologue Martin Heidegger might have somewhat colored her analysis of evil. I mean, she had a reason to dismiss the importance of ideas, propaganda and prominent intellectuals in creating "evil" regimes when she had a connection to such things (just as she and others covered up how much of an overt NAZI and antisemite Heidegger was, even Hitler took power).
See: https://en.wikipedia.org/wiki/Hannah_Arendt#Marburg_(1924%E2...
And naturally this is a controversial take since Arendt and Heidegger have defenders to the present day.