Why would they allow just anyone to edit the article? They probably could be a better process, which goes beyond the scope of Wikipedia, to verify identity but why would they not ask for this?
Wayback machine capture of Wikipedia from Mar 31 2001
> Welcome to Wikipedia, a collaborative project to produce a complete encyclopedia from scratch. We started in January 2001 and already have over 13,000 articles. We want to make over 100,000, so let's get to work--anyone can edit any page--copyedit, expand an article, write a little, write a lot. See the Wikipedia FAQ for information on how to edit pages and other questions.
The nature of Wikipedia has evolved over time as the web has evolved over time. In fact, it followed the pattern of most large web institutions: open and freewheeling when nobody cares, consolidating and conservative as it becomes infrastructure.
Somebody should tell Wikipedia. Their banner still says "Welcome to Wikipedia, the free encyclopedia that anyone can edit."
And we're asking "why would they let just anyone edit a page?"?
So it inevitably becomes that the onus falls on filtering out the crap before it hits (rather than cleaning it up afterwards)… and thus inevitably more policy, bureaucracy and requirements placed up front.
And while anyone can choose to meet these requirements, it becomes cost-prohibitive to learn and adhere for a drive-by editor, whereas it gets amortized out for long-term users. Thus it becomes open to all, yet open to few.
In other words, how exactly is the "common knowledge" separated from the "controversal" one, which requires a proof to present to self-appointed guardians of the True?
Where the king of the article hill would decide.
There is a whole lot of policy and debate behind that rule; for a start see https://en.wikipedia.org/wiki/Wikipedia:Verifiability and https://en.wikipedia.org/wiki/Wikipedia:Reliable_sources