I may not remember this correctly, but first, it is my understanding that by the rules/laws in Hollywood, each actor has to have a clean costume each and every day.
That for the main actors this means many copies, and if I remember it correctly it was very hot working under the old keg lights so sweating was a major problem so an actor could go though a few costumes changes per day.
Not to mention other kinds of mishaps that would call for a change, this is why all real costumes have a zipper of other fastener to allow removing and exchanging without going over the head so that its change will NOT harm either the face makeup nor hair.
Now add in ALL the extras.
The laundry services on the lot are the equal of a major hotel, which often has to change all the sheets and towels DAILY.
Lastly, if they had to remove the rank braid, why not the Star Fleet Emblem on the chest?
It would be just as much subjected to damage by dry cleaning as were the rank brad, if not more so.
Think how many seamstress that would take to remove and replace (sew) on all that rank brad.
I don’t think the brad was removed every day to all those costumes.
My 2 cents worth.
Rich