I dont understand the Oval office comparison.
IT works for children, but for grownups it falls flat.
1) If I went to the oval office I wouldnt wear a tallis and teffilin
2) IF I was there 3 times daily for as long as I can remember and for as long as I have left on this planet.
You can bet I wouldnt wear a jacket
3) In a formal setting (assuming it wasnt 3 times daily) I would wear a tie and suit not a jacket
1) Nowadays we don’t wear them all day, but if you were davening shachris in the Oval Office then I assume you wpuld.
2) The culture has changed nowadays, but there are still many people who wear suits and ties to work every day, why should davening be less important than that?
3) So you should preferably wear a tie and suit to davening. But since this isn’t practical, there is a lesser darga of at least wearing a jacket.