I've found no substitute for getting breaking news on a specific topic (e.g. natural disasters, war, politics, sport). Google News is second best, but the sites it indexes are at the absolute least 20 minutes behind twitter.
Zite was my favourite app from many, many years ago. But it was good at collating daily reading, not for up to the minute/second curation.
For certain topics that are time sensitive, I haven't found anything that comes close to twitter.
Genuine question: who cares?
There is almost no news where the difference between getting it now, twenty minutes from now, or tonight makes a meaningful differ to your life. Much of the information in the first twenty minutes of an event will be confusing, misleading, and/or wrong.
E.g., when I saw police helicopter that seemed to be doing a low altitude search pattern about 300 m away, and a TV news helicopter hovering higher up in the same area, I wanted to know if this was something I needed to be concerned about.
A quick search on Twitter and I found a recent tweet about gunfire in a store in that area and a shooter on the loose.
True for the most part. But occasionally there's good reason to want to know some information sooner rather than later: outbreaks of war, dangerous/breaking events in your localised area, dangerous weather alerts etc.
So to avoid twitter, you can subscribe to the primary source.
At least it used to be this way. But then a few official places that annouce things have turned to use twitter as their primary source.
If CNN has decided not to cover the protest happening outside your downtown office and you don't want to go up to a rowdy crowd to figure out what's going on, Twitter would (have) be(en) the place to drum up intel (with which to decide if you need to go home early that day or not).
I don't really get into the news enough to want a real time feed. Even if I did, I think I'd look for something more reliable than a collection of posts from Twitter users. It probably even goes deeper than not getting into news for me though, because heck, I don't even watch much TV really.
But I am into sports. And I think the best real time sports feeds out there are the reddit game threads. Now maybe the threads on X are better for some people? I don't know? But reddit game threads are far superior for my purposes. ie - Finding out if everyone else is thinking "What The Actual F--- was that?" Whenever Drew Allar threw the ball in a bowl game for instance.
Similar to you not having found a substitute for news over Twitter, I haven't found a substitute for reddit game threads where these kinds of sanity checks are concerned.
The tech is there now for the government and other entities to distribute with open protocols or things like rss, but Twitter never was that