Watching her hold it close, it helps Jor-El conclude that it was the right choice. "It's no more part of a uniform for me than your jacket is for you." A marker of his relative on Krypton, but not a necessary article of clothing- here, at least. "It's only something that's part of my culture." Even though it's much too long for her to wear- and he doubts that Hayley would wear it as intended in the first place- it's something he's sharing with her.

When he has the time and inclination, replacing it will be simple.