Daboss is correct - the finish is dependent on the pitch being thrown. I can't say I've ever seen a screwball finish (RH pitcher to RH batter) with a finish across the body. I agree with your philosophy of teaching beginners the way you describe, especially for control. Eventually on more advanced movement pitches the arm/hand finish will follow the pitch. High for a fastball or peel drop, across the body for a curve, high and out for a screw, straight ahead and low for a backhand change. A high finish for a backhand change will generally produce a hanger - not good.
Anyone who speaks in absolutes should be prepared to fully explain HOW and WHY you should always finish in a certain position. ALL top NCAA women's pitchers have finishes which follow the pitch. There has to be something to that...
Also, there is a lot of proof in watching actual game footage of pitchers (actually all athletes) in action. Although they might say they are doing a certain action, the video will often prove them wrong. They THINK they are doing it, but they actually are not. Nearly all MLB swings are identical from load to finish, and video proves that. However, some players will insist that they are doing something else. But the video doesn't lie.
Klump has some valid points. IMO, women pitchers mechanics are slightly different than men - possibly an upper body strength issue. Women pitchers tend to be more "full body" and legs, whereas men can do a lot more with just the upper body for arm whip. Just my opinion, but I think there are distinct differences.