One of the most common arguments I have seen against 4th Edition D&D is that it has abandoned “pulp style” for “anime style”. Usually this charge is leveled by members of the “old school” community that seem to feel that only books listed in Appendix N can ever influence D&D. I find this charge to be ridiculous. Anime is the modern day pulp. This is quite literally true in the printed form of the style, manga.
Manga tend to be printed on cheap paper in digest sized books. Manga stories are a goofy mish mash of styles with little to no regard for scientific or historical accuracy. This was at the very heart of most pulp adventures in the early part of the last century. Manga stories, especially the fantasy ones, are often violent and tinged with sexuality. Violence tinged with sexuality is the very basis for Conan and his mighty thews. Many people express a love for the baroque, florid writing style of the pulps (time has worn away all the crappy, hack jobs). The best of manga has fantastic, expressive art. Manga, like pulp before it, is the low budget, accessible fantasy of its day. Anime is similar to the old sword and sorcery films in the same way.
Manga is the pulp of today. Having D&D inspired by manga and anime is not some grand betrayal, it is a proud tradition. This is the fantasy of today's high school kids. You cannot expect them to be constrained by seventy to one hundred year old “literary” conventions. Many of those stories have been out of print, or at least not very accessible, for years. Kids today don't know about them. In fact it would be hard for them to know about them. Why should they? They were the low budget escapism of another era, not Charles Dickens.
It is important for D&D to be grounded in the fantasy of the time. In the 1970s it was the pulp adventures dating back to the 30s. During the late '80s and through the '90s it was vast fantasy epics. These were in many ways inspired by the D&D campaigns their creators had grown up with. If fact I would go as far as to say that by the time TSR fell D&D was in danger of sinking into a closed, creativity feedback loop. Fantasy was based on the D&D model which was based on the fantasy it was based on. The introduction of the manga and anime styles is a much needed breath of fresh air.
Kids today are doing exactly what you did. They are living out adventures in a fantasy world inspired by the media they consume. And they seem to be having a good time doing it. D&D is a tool, not a religion.