I like to think I'm reasonably well-traveled, and I've never seen an elevator NOT do that.

However, I think you might be correct about transit systems, where the blocked doors might re-open a small amount before quickly attempting to re-close, to keep the train on schedule and prevent this behavior.

The alternative being closing the doors on the person's arm and likely injuring them to avoid a minor incovenience?

That's the case with most elevator doors, worldwide...? If you put your hand in a closing elevator door, it's supposed to open again.