It's not really about normie or not, but amplification (through number of users) and ease of access. Not just as a reader, but also as a contributor.
SA had a paywall. It had an elitist community that was unwelcoming towards new users, with strict etiquettes shaped by moderators and users alike, and users that were predisposed to forming cliques, along with strictly enforced rules that made it easy to get banned and forced to pay money. One ban was enough for most people to not return, even if they were able to pay. All of these combined to form a significant barrier for new users.
4chan dealt with all of these issues. It was free. It was anonymous, so no one could tell if you were a new user or not, and cliques weren't an issue. There was almost no moderation outside of illegal stuff. The SA community was also very anti-anime, which meant you weren't welcome to be a weeb anywhere other than the dedicated subforum (ADTRW).
So then 4chan gets huge. It's overwhelming for the average person. There's just too much content to sift through. Some of that content is too shocking for the average person. Posting/contributing can be harder for some people who don't want to risk being insulted when they think they are following the informal rules.
Early-mid Reddit ends up being a sort of middle-ground between SA and 4chan. It's free. It's somewhat moderated. It's curated by users through the upvote/downvote system. You need to register an account to post, but you can make new accounts whenever you want (old Reddit didn't require an e-mail), so you can basically be anonymous if you want to. You can further curate and filter content with subreddits. The shocking content is still there for those who want it.
Then Imgur ends up becoming Reddit for people who primarily use mobile devices and don't like Reddit's UI. But the communities exist alongside each other.
A bunch of old SA posters go to Twitter, because it turns out the average Western internet user finds SA posting and humor funny, and the biggest motivation for FYAD shitposting was always attention and building up your "brand". They inadvertently start what becomes known as "weird twitter". SA-style shitposting has now become the standard posting style for people who "get" Twitter.
Between Reddit, Twitter, and Imgur, there's now enough ease of access for your average internet-savvy person to be exposed to a unified Western internet culture, with the flow being 4chan -> Reddit/Imgur -> Twitter, and then Twitter leading to exposure through media like TV, online "journalism", etc..