They used to be de rigueur. Embroidered with colorful show logos and worn by cast and crew members. I can't remember the last time I saw one for a current or recent show.
Heather was wearing that jacket when I stage-doored TCP on Saturday night! I don't recall anyone else wearing it though - and there were no jackets for any of the other shows I stage doored over the weekend (Fun Home, Waitress, Aladdin, Matilda, and School of Rock) - though Allison Case was wearing a "Team Honey" shirt on her last day of Matilda which I found cute.
In recent years, those old school jackets have been replaced with Show Hoodies. I've seen them for Hamilton, Shuffle Along, Waitress, etc. Every show gets a hoodie nowadays.
They are still around for some shows. American in Paris has one, and I think the Crucible even had one (or at least the sold jackets and some of the company bought them)