Digging into it some more, I noticed that many of the default templates do not have a Standard label set for Profiles.
So then I discovered I can delete and rename Label Sets at will, and C3D will not auto-create another Standard set. For us, this means this becomes a non-issue, because so far we've only really found the need for a single Label Set. And if there's only one Label Set in the drawing, it gets used automatically. So all we need to do is delete the Standard Label Set from all our drawings and templates, and we get the behavior we want.
But if we regularly used multiple label sets, this would be more of an issue. I tried deleting and creating Label Sets, and I could find no obvious rule for which set got applied. I thought it might be something simple, like the earliest-created set would be the one used, or the latest-created set, but neither seems to be the case. Then I thought maybe alphabetical, but that doesn't seem to be the case either. So far, it just seems completely random to me as to which set ends up being used. But whatever set it uses, it uses that same one consistently. Deleting or creating Label Sets can sometimes get it to start using a different one, but then it keeps using that same one until you create or delete label sets again.
Sinc