It's worth noting that this is really where the subversion of Evangelion being "more than a mecha show" kicks in and set the tone that this was more than just a kid's show. Now, there had been adult mecha anime in the past - most notably the works by Yoshiyuki Tomino like Gundam, Ideon, and Dunbine, or Ryosuke Takahashi's stuff like Dougram and Votoms, but those were more or less war dramas based around one key ideal - war fucking sucks. At the outset, Evangelion seems like the typical mecha show that was common at the time - self-contained episodes, giant monster gets blown up by giant robot every week. But as the show scratches the surface and each character reveals their true motivations, it becomes more of a study of the human condition and how we interact with others.
Now one of the commonly held beliefs is that Anno suffered a massive depression midway through the series when TV-Tokyo rescheduled it to late nights, which caused the second half of the series to be much different from the first. I'm not sure I put much stock in that though, as Evangelion seems to have a continuous narrative the entire way through. What happened more likely was that End of Evangelion was the original intended ending for the series, but due to the aforementioned timeslot change and other real-world issues affecting Japan at the time, the shows budget was cut heavily, leading to the last two episodes being shown as they were. When the show ended up being a major success on home video and worldwide, Anno got the opportunity to create the ending he wanted, and also gave the fans who sent Gainax death threats the ending they deserved.