Differentiating from others is not a core value of Catholicism. Contrarily, it's claiming to be the default way of Christianity, which is expressed by the “catholic” in the name. Catholicism claims to continue by apostolic succession from Peter by an appointment of Jesus. So, if top Catholics realize that justification by faith alone is an idea from Jesus spread by the original apostles, it is fitting to accept that officially.
I think that the point of the original post is highly unrealistic, but I wrote this because it seems that you miss the point of Catholicism.
Protestantism came from an attempt to reform the Catholic church; it was not meant to be a separate thing until the reformers were excommunicated. You shouldn't think about Catholicism as necessarily separate from reformed traditions i. e. protestantism. It is clear from what Jesus said that church unity is good, so, if Christians were more united on doctrine, the world would be better IMO.