“The differences between these two major types of Christianity, at the present time, involve contradictions,” wrote Avery Dulles in The Catholicity of the Church. “Full unity cannot be achieved by convergence alone but only by conversion.”
Dulles believed that the necessary conversion could only take place if each church engaged the other: “each ecclesial body must both give and receive the greatest measure of enrichment and correction that it can through mutual witness and dialogue.”
I think Dulles is right, and Protestants ought to listen. But of course, the problems start when we start asking what is “proper.” Here is his summary of how Catholics answer the question: “Roman Catholicism, committed to the principle of visible and symbolic mediation, is convinced that any church lacking the full sacramental, hierarchical, and dogmatic structures, including the papacy as defined at the two Vatican councils, is institutionally deficient.”
That, for Protestants, is part of what Catholics have to convert from.