Why is this a problem? There is only one reason in business why you'd want to grab the attention of the average person...and that is advertising .
Will SpaceX start advertising during launches? Maybe...up until then being known to the average person is not an advantage.
Some people claim going public would enable SpaceX to cash in on its fame by offloading loads of stock to the aforementioned normies...but that practice scares away smart/value money so again...until SpaceX starts advertising during launches the only person benefiting from the social media fanfare is Musk who gets to be invited on SNL to show how socially akward he is.