Good question!
I leave mine, then they wonder out and I look silly. There's always a good soul during some social gathering to "kindly" let me know one is hanging out, and I've even been told, twice, in the low understated between-you-and-me-and-the-gatepost tone, "These are meant to be cut out upon purchase, dear" (geez). Tiny pins would be a solution for non committers like me (unable to commit to cutting them off), but on certain garments pins would show through the material.
There's also the problem of ironing, I don't know if you're old fashioned like me and still iron, I do, and then I've ruined items (and the iron plate) by inadvertedly run the iron over the clear plastic strap which immediately melted into the fabric and the iron. Ugh.
Those straps are becoming longer and longer, sometimes I think it's a bad joke.
Gryffin, I am intrigued: how do you "use" the straps with delicate necklines? Do you mean when the garment is hung or when you wear it? Just wondering