Could you elaborate on that? (I'd heard people talk about a decline but not this as a reason)
Anime is not declining, and Evangelion (a 1995 series) isn't responsible for any decline in popularity that the medium had over here in the 2000's. Otaku-pandering and the "moe crowd" in Japan are nothing new.
Relevant cherry-picked comparison:
In the 90's and early 2000's, American fans didn't have the instant access to currently-airing anime shows that we do today. As a result, we only got a partial picture of what the industry was producing back then - consisting of the stuff that was on US TV and what was available on store shelves. The build-up to that era of American anime fandom was the early fansubbing trend, where OVAs (original video anime) on unofficial VHS tapes were circled around early fan groups and given fan translations.
Nowadays, we get legal streaming of most current shows just hours after they premiere in Japan, giving us the best modern anime along with the crap. So, long-time fans who weren't exposed to (or forgot about) the less-than-stellar anime of bygone years end up viewing the past through nostalgia goggles.
Without Cartoon Network and its Toonami and Adult Swim programming blocks, anime probably wouldn't be as popular in the US. Sure, other networks could include anime in their line-ups, but I can't really picture Nickelodeon/Disney Channel/Sci-Fi giving the medium as much exposure as CN did. The internet-based fandom will of course still exist, albeit on a smaller scale.
The thing about American TV is that, AFAIK, the networks and channels prefer to have content that's under their editorial control - and anime, being a foreign thing made for Japanese viewers first, doesn't mesh too well with that. This is why many of the early runs of anime on US airwaves had the shows become heavily edited and censored - from "Star Blazers" and "Robotech" to Sailor Moon and whatever 4Kids got their hands on. It's also why we even have American remakes of certain UK shows, despite the originals being in the same friggin' language.
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Regarding the impact on American/Canadian animation in a world without CN: Well, certain OTL industry figures obviously wouldn't get their big breaks - at least not in he same manner.