No, my argument is a bit more subtle than that.

That is, the arguments for the good of free speech do not extend to Twitter because of the ways in which Twitter is broken.

Tweets are certainly speech. Banning certain content is certainly a restriction of free speech. It's just that the social environment of Twitter is critically different than venues for which the merits of free speech were worked out, so the arguments in favor of free speech mostly fail to go through--the premises are not met. (Mostly they weren't explicit premises to begin with; rather, people had an idea of what free speech was like, and argued based on that idea. But what Twitter is like is different.)

For instance, John Stuart Mill's seemingly incredibly strong principle of harm:

the only purpose for which power can be rightfully exercised over any member of a civilized community, against his will, is to prevent harm to others

blithely admits Twitter bans on Covid misinformation, because the misinformation literally can do harm to people who are fooled by it, and counterarguments about finding alternative information are much less compelling when Twitter busily groups anti-vaxxers with each other, giving the illusion of consensus by its own mechanism of selection, and reducing the ability to encounter a meaningful opposing position (thus rendering it much like "crying fire in a crowded theater"--the ability to use normal mechanisms to check the veracity of the information is greatly reduced). Likewise, Mill's endorsement of free speech as a way to determine truth is completely undercut by Twitter's mechanic leading to lies being more rapidly and widely spread than truths. (It's not really Twitter's fault per se--it's us--but taking account of the flaws of users is just as important on Twitter as is taking account of the flaws of drivers when designing cars and roads.)

So, basically, speech on Twitter doesn't work enough like pre-social-media speech to take advantage of the arguments in favor of free speech.

You can use different arguments...but really, Twitter and social media needs some pretty serious fixing, because those arguments ought to work for Twitter; those benefits of free speech were important. We needed that.