The OP raises the valid point that the context of social media has shifted the balance of the impact of people being free to lie, increasing the ratio of harm to good that this protected freedom results in.
But that thesis, which I think has merit, is separate from whether there is any viable solution that is even worse than this increasingly negative result of the freedom to lie.
The following is my own basis for supporting free speech, and seems consistent with sentiments of Jefferson and Enlightenment principles generally:
Coercion will tend to favor untruth because the truth can defend itself and can reach acceptance via the evidence that supports it reaching the minds of the masses, under the assumption that on the whole and in the long run the majority will come to accept what reason dictates. And even if the majority do not engage in reason, there are countless untruths competing with each other but only a single truth. Thus, on the whole the truth stands a better chance than any one untruth. Although on a particular topic or moment in time this may not be the case, on the whole, and especially regarding matters where what is true impacts each person's quality of life, the truth will tend to win out if all information and ideas are allowed to fairly compete for acceptance.
That said, I do agree with the OP quote that social media give misinformation an advantage. My take is that this occurs b/c it increases people's exposure to misinformation, often seriously harmful if not deadly, without negative consequence to the source of that misinformation. With traditional media, lies tend to be costly in the long run. They may garner immediate attention but they lower credibility of the source such that anyone interested in accurate information won't tune in. Only limited specialized outlets trying to corner the market on feeding irrational dogmatist what they want to hear (Fox News) can profit from a lies over credibility model. But social media is not "a source". It's a platform where largely anonymous sources spread information that just pops up in front of people when they aren't even looking for information. The original source is often layers deep and not known to the person who sees the information. People don't view FB as the actual source, so they don't get blamed and thus are not harmed by profiting from helping others to spread lies. Besides, FB serves so many functions for people besides an information source that they won't stop using it even if they recognize it as a bad source of political information, and while using it will inherently be exposed to such information.
However, I don't see any good solution to that problem that in any way involves changing how the 1st Amendment is understood or applied.