Flying commercial wouldn't gain Musk any anonymity. The second he sets foot in a public airport social media of all forms would be flooded with photos of him, what gate he's waiting at, etc. And that's MUCH worse for Musk because everyone and their uncle can see what gate the flight he boarded is going to disembark at, meaning a crowd of people with less-than-kind intentions would have time to gather there in advance of his arrival.