The Foundation pursued this idea before. The idea initially received a chilly reception from the community. The team built it anyway. On deployment day there was an epic-level manure explosion and the project dropped stone cold dead.
First I'll address the chilly reception. Everyone is familiar with social networks. It defines a large portion of the internet. Wikis kinda resemble social networks. You've got a big community of people.... on the internet. Except our purpose is very different. If a social network is like nightclub, wikis are like an office space. The expectations and culture are very different. We find it disruptive to our work when people show up and behave as if the wiki is a social network. We firmly reject any characterization of the wiki as a social network. On EnWiki we have a policy link dedicated to this: WP:NOTSOCIALNETWORK.
We're not a social network, and we don't want the wiki to resemble a social network. Anything that makes the wiki look more like a social network increases the likelihood that people will treat it like a social network. And as I said, that disrupts our work. We tend to be extremely skeptical when the Foundation initiates any work which is inspired by social networks, or which makes the wiki look more like social networks.
And to be honest, we look down on social networks. We're doing important work to benefit humanity. We can have a snobbish disdain for social networks, and a disdain for anything with a whiff of making the wiki resemble a social network.
Then there's another point. A lot of things about wikis do initially come across as unusual and unfamiliar for new users. However the concepts of a wiki very quickly come together in a very simple way once people start editing. What's a wiki? It's just a bunch of pages. What's a page? It's just a text file with a title.
What's an article-talk page? It's just an article-page with a different tile. When you encounter an article-for-deletion discussion page for the first time, it's not really new. It's just an article-page with a different title.
Once you learn a little bit of editing, a page quickly becomes a very powerful and flexible thing. Anything that works in one place works exactly the same everywhere.
What's a userpage? It's just an article-page with a different tile. It's whatever you edit it to be.
Skydiving is a weird hobby, most people don't enjoy jumping out of airplanes. But if you run a skydiving foundation, that is your target audience. If you run a wiki foundation, your target audience is people who think editing-an-encyclopedia is a fun hobby. Your audience think it makes perfect sense to use a wikipage as a userpage/profile.
And here's why the last project exploded in a spectacular fashion: Staff have a bad habit of thinking it's a neat idea to add a pretty PageImage() whenever the software mentions or links to a page. Are we showing article editing suggestions? Let's toss pretty PageImages on it! Are we showing recently edited articles? Toss pretty PageImages on it!
As editors, we have a very different view. First, we don't toss decorations on links to make them more click-baity. We have no interest in maximizing clicks to maximize advertising revenue. But more importantly, we are acutely aware that our images are WP:NOTCENSORED. When the software blindly retrieves a PageImage(), it may be retrieving an image of an asshole, a vagina, fetish-bondage, a string of semen running across a neckline, anal fisting, an image of Muhammad, Piss-Christ artwork, a maggot-infested wound with exposed bones and tendons, the mangled bodies of warcrime victims, or anything else. Britain even imposed a nation-wide block against one of our PageImages as alleged illegal child porn. See en:Internet Watch Foundation and Wikipedia for encyclopedic coverage of the incident. (Or don't see the article, the image involved is reproduced there.)
When the profile page was deployed it included a list of recently edited articles... with PageImages of course. On deployment day, people who had edited completely random pages to revert vandalism discovered they now had shiny new profile pages.... with pictures of human genitals. Those community members didn't like the idea of a profile page to start with, and they were none too pleased with the result. They went to the Executive Director's user_talk page to explain why they were unhappy. They they thought it quite reasonable to illustrate their complaint with screenshots of their profiles. One screenshot had a pair of penises. The other screenshot had a lovely bleached asshole and neighboring vagina. Posted on the Director's personal user_talk. Lila handled it gracefully, although it would have been hard for her to blame the editors. That was the last I heard of the Profile project.
Well, that was the last I heard of the project for four years anyway.