I think you're on to something, but maybe in reverse. You see, the white "outfit" Tron sports is no mere cosmetic addition like the clothes you and I wear. It is literally his base code. In the cartoon, it's supposed to represent his 1.0 appearance from the first movie. I see it as such: with the damage Tron took from Clu, the only way to survive until he established that Fortress of Solitude and healing chamber was to revert back to his 1.0 code, a "deeper" level of his identity.

When he exchanged disk halves with Beck, he was actually giving Beck his basic 1.0 code. Outdated, for sure, but more than enough for Beck, who was never programmed for system security in the first place. Therefore, Tron has to permanently assume his "black outfit" that clearly shows the scars when he is not healed.

Your theory would work better if we had seen Tron take off and reassemble his disk when he revealed his true identity to Beck. Instead, he seems to go from Rinzler appearance to classic Tron in an instant. I think the Rinzler persona is more of an outfit than the white suit. That's how I perceive it, anyway, but for all we know, the show creators might have an entirely different explanation...or none whatsoever.