getting the arm across is irrelevant to finish the choke if you have gotten the 90° angle, the thing is, unless you have long legs, like really long lengs, if you have average for example, its quite difficult to lock it up if the person is really big. Also, for sd purposes, getting the arm across is a good habit to make, you cannot get bitten out of desperation, and the triangle is about the safest sub to go in a SD situation. So I explain to my students what does the arm across is for, when is a must and when is not.
AS you said, some people like to keep the arm going across because there are a couple of escapes that can be done with the arm all the way across, but those dont really work if you have gotten the angle before they start doing the escapes... may be escaping through the back door can be done in the process of locking it up, but onces is locked, that option goes out of the window...