If you had told me several months ago, immediately after Elon Musk bought Twitter and Ron DeSantis celebrated a thumping re-election victory, that DeSantis would launch his presidential campaign in conversation with Musk, I would have thought, intriguing: The rightward-trending billionaire whose rockets and cars stand out in an economy dominated by apps and financial instruments meets the Republican politician whose real-world victories contrast with the virtual populism of Donald Trump.

The actual launch of DeSantis’s presidential campaign, in a “Twitter Spaces” event that crashed repeatedly and played to a smaller audience than he would have claimed just by showing up on Fox, instead offered the political version of the lesson that we’ve been taught repeatedly by Musk’s stewardship of Twitter: The internet can be a trap.

For the Tesla and SpaceX mogul, the trap was sprung because Musk wanted to attack the groupthink of liberal institutions, and seeing that groupthink manifest on his favorite social media site, he imagined that owning Twitter was the key to transforming public discourse.

But for all its influence, social media is still downstream of other institutions — universities, newspapers, television channels, movie studios, other internet platforms. Twitter is real life, but only through its relationship to other realities; it doesn’t have the capacity to be a hub of discourse, news gathering or entertainment on its own. And many of Musk’s difficulties as the Twitter C.E.O. have reflected a simple overestimation of social media’s inherent authority and influence.

Thus he’s tried to sell the privilege of verification, the famous “blue checks,” without recognizing that they were valued because of their connection to real-world institutions and lose value if they reflect a Twitter hierarchy alone. Or he’s encouraged his favored journalists to publish their scoops and essays on his site when it isn’t yet built out for that kind of publication. Or he’s encouraged media figures like Tucker Carlson and now politicians like DeSantis to run shows or do interviews on his platform, without having the infrastructure in place to make all that work.

It’s entirely possible that Musk can build out that infrastructure eventually, and make Twitter more capacious than it is today. But there isn’t some immediate social-media shortcut to the influence he’s seeking. If you want Twitter to be the world’s news hub, you probably need a Twitter newsroom. If you want Twitter to host presidential candidates, you probably need a Twitter channel that feels like a professional newscast. And while you’re trying to build those things, you need to be careful that the nature of social media doesn’t diminish you to the kind of caricatured role — troll instead of tycoon — that tempts everyone on Twitter.

That kind of diminishment is what the Twitter event handed to DeSantis, whose choppy launch may be forgotten but who would be wise to learn from what went wrong. There’s an emerging critique of the Florida governor that suggests that his whole persona is too online — that his talk about wokeness, wokeness, wokeness is pitched to a narrow and internet-based faction within the G.O.P., that he’s setting himself to be like Elizabeth Warren in 2020, whose promise of plans, plans, plans thrilled the wonk faction but fell flat with normal Democratic voters.

I think this critique is overdrawn. If you look at polling of Republican primary voters, the culture war appears to be a general concern rather than an elite fixation, and there’s a plausible argument that the conflict with the new progressivism is the main thing binding the G.O.P. coalition together.

But it does seem true that the conflict with progressivism in the context of social media is a more boutique taste, and that lots of anti-woke conservatives aren’t particularly invested in whether the previous Twitter regime was throttling such-and-such right-wing influencer or taking orders from such-and-such “disinformation” specialist. And it’s also true that DeSantis is running against a candidate who, at any moment, can return to Twitter and bestride its feeds like a colossus, no matter whatever Republican alternative the Chief Twit might prefer.

So introducing himself in that online space made DeSantis look unnecessarily small — smaller than Musk’s presence and Trump’s absence, shrunk down to the scale of debates about shadowbanning and Section 230 of the Communications Decency Act. The Florida governor’s best self-advertisement in a primary should be his promise to be more active in reality than Trump, with his claim to be better at actual governance made manifest through his advantage in flesh-pressing, campaign-trail-hitting energy.

The good news for DeSantis is that he doesn’t have billions invested in a social media company, so having endured a diminishing introduction he can slip the trap and walk away — toward the crowds, klieg lights and the grass.

For Musk, though, escape requires either the admission of defeat in this particular arena or else a long campaign of innovation that eventually makes Twitter as big as he wrongly imagined it to be.