I see so many men leave their jacket arm hanging when wearing tfillin, even though we are supposed to dress as if seeing a king. I understand that some jacket arms sleeves may be tight, but I always have ensured mine were large enough. People even buy special raincoats to cover their fedoras, etc. So, do these same men leave their arms sleeveless when going to work, job interviews, court, etc.?

ב"ה Shalom I can see your point of view, however most people do their best to make sure they get their arm into the sleeve. I am not giving a ruling, but I personally don't see people leaving the jacket arm hanging as severe as someone dressed improperly for Davening. Although, it would be better that the arm is in the sleeve in place, leaving it out is not done out of disrespect, but due to circumstances which make it difficult. The people who do so are fully dressed for Davening and putting on Tefillin, but have one shortcoming of being unable to get their Tefillin in the sleeve. All the best