No online global discussion mechanism arisen to replace Usenet because there is no economic incentive for such a thing to exist.
It helps to ask the question, "why did Usenet exist in the first place?"
In the days before web browsers and before ubiquitous connectivity, the state of the art for engaging in electronic discussion was the dial-up bulletin board system. These systems generally had limited offerings, and a lot of them maintained overlapping subject matter with other systems. Long distance phone rates made calling made distant boards impractical. Discussion was typically local.
Email overcame the long distance call problem, with either hop by hop UUCP or direct-over-the-net SMTP. Mailing lists could emulate a discussion board, but they were, by definition, closed. Mail quotas were miniscule, reflecting the cost per megabyte of the day. Large mailing lists made mail server admins crazy, since replicated messages from a mailing list rapidly ate into mail spool space.
Usenet stepped in to fill the void by providing a public hierarchy of discussions that operated like open mailing lists while using less disk space. Usenet used transport mechanisms similar to mail (UUCP or NNTP) and allowed cooperating systems to replicate messages. Disk space and bandwidth usage could be controlled by picking the hierarchies of interest and managing how fast articles expired.
But Usenet's success was part of its its undoing. The list hierarchy exploded into deeper and deeper trees. No user or usage management existed due to Usenet's decentralized nature. Spam and trolls grew out of control and the signal to noise ratio became unbearable. Like SMTP, no sender authentication existed and the emergent ad-hoc security mechanisms devolved into fights among the most persistent.
The last newsreader I used when I read Usenet on a regular basis was called "nn" - Their motto was "No news is good news, but nn is better." The stated objective of nn was "NOT to read news," which reflected the fact that even as early as 1989 it was difficult to find the wheat among the chaff in the growing sea of sludge that was Usenet.
In the mean time, universal connectivity began to appear, and sophisticated web sites multiplied. Tired of the spam and trolls, people serious about having discussions retreated to a well managed walled gardens related to their interests. Text based discussion was no longer enough for most communities. Adjunct knowledge bases, blogs, databases, images or video archives turned out to be interesting adjuncts to discussion, depending on the topic at hand. Usenet had no modular mechanisms to grow in such a way, and could not adapt was fast as custom built web sites.
Content management of the walled gardens surpassed Usenet in leaps and bounds. People desired (and got) search capabilities and deeper storage than the article expiration window. User authentication and a foolproof banhammer mechanisms helped to keep discussion useful and sideline griefers and trolls. Different software systems evolved to maximize creation and consumption of content in the context of specific topics.
It turned out that people don't mind going to different places for discussion on different topics, especially when the content is well curated, the community is well behaved, and the presentation is optimized to the content at hand.
The social "feedback loop" that has evolved in discussion forums has also added value, allowing crowdsourced rating of content and crowd silencing of trolls. Different audiences have different value systems, so people will tend to gravitate to a place that supports their value systems. A universal online discussion forum might not provide a safe space to discuss controversial topics; the sharding of discussion becomes a feature in that case. (We can have a separate discussion about whether this is good or bad for society as a whole, but that's probably a whole Quora post by itself.)
I agree with Jimmy Wales - reddit is probably the closest thing we have to Usenet, and I never use it. I would also suggest that the troll population has found a cozy home in places like 4chan. Lots of big clusters of discussion still exist, but greater size leads to unbearable noise.
I think the Quoran asking the question may remember a time when Usenet was small and populated by a relatively homogenous population of academics, prior to
Eternal September. The need is not for a universal discussion group, but a community of thoughtful and polite people to engage in discussion. And this is precisely why there is not a universal point-of-entry for discussions. I can argue that Usenet actually proved that point.
To summarize:
Usenet is a relic of another time which grew out of the technical limitations of the era. It was an improvement over the state of the art, but ultimately imploded as its success exposed its fatally weak foundational assumption that people could be trusted to be well behaved in large, anonymous groups.
A universal discussion forum covering all known topics is not very economically viable (or even technically feasible) due to the wildly diverse nature of each topic stream and the personality types that want to have those discussions.