Evangelion might be the only anime to do horror right and it ain't even horror.
My first exposure to the series was an AMV* of a Porcupine Tree song with most of the clips coming from the last few episodes where things get wild and I remember being really shaken by it, so you might have a point.
*unrelated side note my brother is four years younger than i am and when i mentioned an amv one time he had no idea what they were, it was very weird to me how prevalent they were for my internet timeframe/experience to basically not being a thign