But it wasn't and was unlikely to ever be because of the FCC's limited regulatory abilities. The fairness doctrine as some magic wand was always a bit of a myth. Because enforcement was optional, it was more often used as a political tool to shut down content rather than expand it. It also had unintended consequences, like allowing Big Tobacco to counter news reports that smoking caused cancer with propaganda.
"Social media already has a type of fairness doctrine built in because it goes both ways. "
That's not even remotely true, because the platforms aren't regulated and people like Musk can shape them in pretty much any way they wish. Suppressing opposing viewpoints and promoting bigotry and ignorance, as Musk is quite clearly doing, are the opposite of balanced. You think X/Twitter is "fair" at the moment? Facebook during the 2016 or 2020 campaigns or when they were collecting data and selling it to the GOP?
"The Fairness Doctrine wasn't designed to stop guys like Limbaugh"
Again, enforcement was optional, so as far as people like Limbaugh go, it was mostly useless. The stations could be required to provide counter-programming, but there were usually no strings attached. They could broadcast a counter-point at 2:00am and technically meet the requirements, but often weren't even required to do that.
If it couldn't address cable news and couldn't address social media and couldn't deal with people like Limbaugh, it didn't really matter if it was in place or not once all of those proliferated. An entirely new regulatory framework would need to be created to address those, with much tougher regulations and media requirements.
Lessons for social media from the Fairness Doctrine from the Columbia Journalism Review:
https://www.cjr.org/opinion/social-media-fairness-doctrine.php