You bring up Alex Jones, which is a good use case to consider.
Jones was rightfully sued by Sandy Hook parents for defamation. He lost and they won:
https://www.nytimes.com/2021/10/01/us/alex-jones-lawsuit-sandy-hook.html
In March, a jury will award damages, and probably put him out of business.
One thing we need to look at is the promulgation of blatant lies by so-called news services such as Fox. We can't shut them up - too dangerous a precedent, but we can re-introduce the Fairness Doctrine to impose opposite opinions on outlets with large audiences.
Shouldn't be a big deal, and it would affect MSNBC as much as it affects Fox.
And when people like Alex Jones damage other people the way he did, sue them. He didn't even bother fighting the case. He knew he was toast.
But there is no government entity that should or can "regulate" free speech, aside from a Fairness Doctrine that insists on alternative viewpoints. And even that would be a tough sell to a lot of people.
I understand where you are coming from, but imagine a Trump like figure in power who determines who any kind of new approach towards free speech applies to.
Tucker Carlson should also be facing lawsuits for his lies. It's sad that we have to rely on some rich person to do it, but I would hope that some rich person who has been directly affected by his lies, especially regarding vaccinations, sues the pants off him and puts him out of business, like Peter Thiel did with Gawker.