When was the first usage of 'white light' censorship in anime?
TV Tropes has a page on the shadow censorship, which is essentially the same thing. The basic idea comes from overall censorship laws, such as exist in Japan. As this article mentions, a common means of censoring genitals is a "mozaiku" or mosaic, which is pretty much just a pixelization of the area. This page talks about the airbrushing over of female genitalia in pornography magazines.

The white bars (or shadows) seems to be, from what I can tell, attempts to censor genitalia (and sometimes violence/gore) in relatively unobtrusive ways. Shadows and light flares can more easily pass for being just a part of the scene than random people's faces, black bars, blurring, or pixelization. Similar things happen in this, for example, where clouds obscure Naruto's jutsu.

The light flares are also sometimes used to block faces or people, especially in pictures, though that it more of an in-universe censorship (when they're dead or need to be kept a secret, etc.) than censorship because of the law.

As for why not all of them are done in the way that the Neon Genesis Evangelion scene was done, I have two answers. The first is that it is often done for laughs or to add comedic effect, which is not necessarily what is being aimed towards in gory or sexy scenes. The second is that it is not always practical. A lot of work would need to be put in to making some scenes be able to always have something in front of the genitalia or wounds of the character, while light bars, shadows, or clouds are a lot easier.

As for which anime had it first, I currently can't find that, but I thought it would be more helpful to post this at least.