General Discussion

Intimidation tactics are not always used for the express purpose of winning. Sometimes they’re used as a show of strength. Sometimes they are used to mitigate damages, perhaps here in the form of at least one dissent that can support a future legal reinterpretation or some statement in the decision that keeps this issue alive politically. I think, as you pointed out, the main reason he showed up is so his voice on this matter is as loud as the reporting on the oral arguments. It rallies his base and also shows he will stand up to the Court. It’s also a nice distraction from Iran for the media until his speech tonight.
I think your other point about being the “first” is also important not just because he can plant his flag, but he’s trying to show an unprecedented Presidential influence over the other branches of government. Of course, it could be as simple as he saw a mobster intimidate a witness or officer of the court by his presence in a movie or series and thought it looked cool.