It seems like about 1/2 the time when I see clips of the President on US news pieces, he’s yelling over the sound of a helicopter turbine. I would say it doesn’t seem “presidential”, but I guess a lot of the things he does aren’t… it does seem strangely undignified though. Is there some travel thing he’s involved in that means the only time the press has access to him is 5 minutes before his flight leaves every day? Is it just a good excuse not to hear a question and run away? 
Exactly this.
Ronald Reagan was a master at this. Take a look at the sequence in this clip.
Waves to reporters, smiling
Taps his watch - sorry, no time for questions - still smiling
Waving some more, always smiling
Taps his ears - oh, so sorry, I can’t hear anything you’re saying - but smiling all the way
Climbs on board the helicopter with one final smiling wave.
No wonder people loved him.
Trump basically never does press conferences (just 1 solo press conference since he took office), so the opportunities for the press to ask him questions are more limited than typical presidents. When he uses Air Force One, the Presidential plane, he gets to its location at Andrews Air Force Base by taking a helicopter, dubbed Marine 1. Reporters gather behind a line and are able to shout questions at Trump whenever he walks to the helicopter; whether he stops to answer them or otherwise make a statement is up to him. Given his tendency to limit other discussions with reporters while on camera, we get a lot of footage of these moments.
Your last question nails it: He is too cowardly to face reporters/questions except over the din of the helicopter. Our so-called president is a coward.
“Mr. President, do you have any comment about the Secretary of State calling you a Moron?!?!”
If he didn’t yell, you wouldn’t be able to hear him over the noise of the helicopter!
It’s not that he’s always yelling over a helicopter.
When he yells under a helicopter no one can hear him.
Observer bias.
It’s another burger delivery.