Interesting concept, though I totally disagree...
While you claim that you wouldn't be able to tell if you were bowling over or round the wicket, I think subtle changes of angle does make a difference. As a fellow slow bowler I thought you'd have understood this. If the ball isn't turning much subtle changes like changing pace and where on the crease you bowl from can make all the difference.
Changing angle in the delivery stride - ie unpredictably coming close or going wide of the stumps - is a valid tactic, because the batsman doesn't have time to change his set-up, so you are creating an angle between the direction of his set-up and the direction the ball will be coming from.
But switching from over to round the wicket does not achieve a change of angle relative to the set-up of the batsman, because the batsman is told by the umpire that you are switching sides, and thus (assuming he is over the age of 10 and vaguely knows what he's doing) switches his alignment to match.
"To disprove this theory I propose you bowl 4 "up and down" deliveries, not aiming to "do anything" with the ball, pitching the exact same place - say on a good length in line with middle stump.
Bowl 2 deliveries over the wicket and 2 deliveries round the wicket. One from wide of the crease and close to the stumps.
Assuming all the balls pitch and carry on straight, if your theory were correct all 4 would end up in the same place. However in reality they wont, will they?"
On the contrary, if I bowl 4 straight balls on the line of middle stump, then they will all hit middle stump by definition, because that's what "on the line of middle stump" means. I could bowl the ball from backward point, that fact would still be true.
What you mean is they wouldn't pitch on the line of middle stump as seen by the umpire. But that is only relevant for lbw decisions. It doesn't actually factor into how the batsman plays the ball at all.