You're afraid to drive in them??
Anyway, sun bleaching will definitely lighten them, but it will be unevenly, and it will bring out more of the reds and then that will softly fade into more brown tones. My experience has been that they are as purple as they are going to get new, anything else you seeing is either a result of lighting, photography, or batch to batch variance in the leather as it is a natural product that is dyed by hand.
That being said, I sunbleached the pair that I'm wearing today, because they are more of an experimental and rugged boot for me, not a dress shoe. I don't think I would sunbleach a dress shoe, but I actually like the color variance I achieved with these boots. Please note that the changes in colors shift greatly depending on the lighting and the angle you view it from and that is not captured in a still photo.
Also, sunbleaching temporarily got rid of the Cordovan smell, but it returned about a day later and after having the boots for over a year is still present, though less pronounced. The smell has persisted much longer than any other leather.