I have a beautiful pair of antique 1930s sleeve garters with embroidered blue and gold covers which I was fortunate to pick up at a flea market many years ago for about £5. I don't wear them often (only if I'm wearing a shirt with French cuffs and very loose, ballooning sleeves), but there is something satisfying about adding such a classic detail to a well put together ensemble. Same with braces as you say, although for me nothing beats a pair of trousers with incorporated side adjusters.

Armbands are for those who have shorter arm length than the shirts sleeve. The armband keeps the shirt sleeves on the right place so the sleeves dont look longer.

I believe the correct term is "sleeve garters" (I have never heard "armbands" being used in this context, it might be an American thing). They're not really used that much any more- as with many things, they have gone from being a practical tool (in this case used by bartenders and card players as well as other people who used their hands a lot to keep their cuffs from getting in the way) to an obscure fashion accessory.* I have a beautiful original 1930s pair I picked up years ago in a flea market for next to nothing, which I do wear on occasion, if my shirt has particularly long, ballooning sleeves. There is something satisfying about putting them on, I will admit. *Same for the bow tie, which was originally designed for scientists, jewellers, snooker players and other people who would be spending all day bending over a table engaging in an intricate activity that required neckwear that would not flap about and cause a distraction.

Shannmeister I think they are just setting up for the show. When it’s on they will be all dressed up