Despite the unlikeliness of such a series to spawn, it's definitely fun to think of how a Godzilla anime would work.
I like anime, but I am VERY, VERY picky with what I watch. I don't like anything too dorky, or too sexual related. I enjoy anime such as Blood+, Eureka Seven (including the sequel series, Eureka Seven AO), and Cowboy Bebop - you know, series that have a cohesive story and do not rely on much fan service or dorky humor to keep people interested. In a hypothetical sense if a Godzilla anime should be made, I'd like it to have a very engaging story with human characters that are likable and interesting, as well as having a good amount of kaiju action.
Personally I would not mind seeing a Godzilla anime series that is treated like the Showa series. It would definitely work, but it would need to have continuity between episodes rather than just having the 'Monster of the Week' formula that the past Godzilla animated series had which had no sense of continuity between them. Also an idea like Matt Frank's Godzilla Neo would really work too as it mends together all the eras together into one continuity, which makes sense.
Seeing how most action and mecha anime are treated nowadays, and setting aside the stereotypical dorkiness associated with the genre, a Godzilla anime would be a really good idea, which I think Toho is missing out on. It would definitely add new fans to the franchise if an anime on the Big G were to be made.
Unfortunately with Toho's execs all having sticks up their rears, that idea will NEVER see the light of day.