My opinion would be to cut out the lead on the right as it appears to have many more branch union issues. I am basing this on my knowledge and history of included bark unions. I have cut that much, and more, out of young trees and they are still alive. In the trees lifetime this union, and others like it, will help shorten its life.
Yes it should have been done along time ago. If it is slowly reduced to adhere to the 1/3 idea than the final cut will only be larger and more inviting to decay.
If the tree was a columnar than I would say leave it alone but from the pics it isnt. It would appear to be a nursery tree that had its apical meristem broke either by mother nature or my first guess would be a propagator that didnt go back and do corrective pruning before the sale. How many of those have ya seen? On that note some nurseries will knock the top off so the tree has "more leaves" and they have more stock to grow. To the average Joe a fuller tree is a better tree. To the tree it is set up for a shortened life.
danr posted a pic and question and I offered my ideas based on my personal experience and arborcultural training. The beautiful thing about nature is it didnt read the book and has a very strong desire to live.
I would also address the root flair issue and whatever else you find down there. Thats a whole new can o' worms.