The site has had tons of "basic one-shot" SCPs. So much so that trying to make one stand out is a goddamn accomplishment, as the format for one leaves little room for error. We have dozens of monsters that kill you, how can yours stand out without a story or significance?
It's not so much that a SCP needs a story so much that a SCP is too boring if the author can't get it to work using only its core anomaly.
Story makes it easier for a SCP to stand out, because it doesn't solely rely on the force of the core anomaly. The author has room to make more errors, and the reader is more forgiving of any that may crop up.
In a sense, SCPs without story have wrapped around to the point where the best writers are likely to be the ones who can do it. They aren't flashy, but it takes a lot more technical skill to pull off than it looks.
SCP-527 works because it criticizes the idea of SCPs needing stories on a meta level.
SCP-2365 works because of the author's skillful use in creating a sense of "creepiness" and skillful balance in executing a random-event anomaly.
SCP-2301 works because the author conjures vivid imagry in the description and workings behind what is otherwise a classic "thing what kills you".
Case in point: I'm betting that if you had 100 newbies and told each of them to write up three SCPs about "a guy with a fish head", "a bear trap that kills you in the night" and "a thing that transforms between a dragon and an oni, and can only be defeated by samurai or knights", we'd get about 300 articles that can't make it on the site.