Catholics don't call themselves "Romanists" -- although I think the reasons given by Protestants for using that term are accurate. And for that reason, I don't use the term "catholic" or "universal," in an unqualified way. Roman Catholics have cast their lot with Rome and are stuck with it -- they have wrapped themselves in it, and the provincialness of that term necessarily accrues to them. If it is uncomfortable with them, that is just what they have chosen.
Yet, "Roman Catholic" is a preferred designation, somewhat officially. For example, my 1927 "Explanation of the Baltimore Catechism" asks, in Question 118, "Why is the Pope, the Bishop of Rome, the visible head of the Church?" And the answer given, "The Pope, the Bishop of Rome, is the visible head of the Church because he is the successor of St. Peter, whom Christ made the chief of the apostles and the visible head of the Church."
And the explanation:
"Of Rome." That is why we are Roman Catholics; to show that we are united to the real successor of St. Peter, and are therefore members of the true apostolic church." (Rev. Thomas L. Kinkead, "On the Church," from "Explanation of the Baltimore Catechism,) (c)1891, 1921, 1927 New York: Benziger Brothers, "Printers to the Holy Apostolic See," pg 131).It really is a fascinating work. It might clarify some things to cite more of it here.
More recently, in his 1987 work "The Catholic Moment," Richard John Neuhaus, convert par excellence, writes of his decision to to use the designation "Roman Catholic" throughout that work:
I have generally written Roman Catholic, and there are three reasons for that. First, in Christian history, catholic is frequently synonymous with orthodox, and it would be both rude and wrong to suggest that Roman Catholicism has a monopoly on orthodox Christianity. Second, many non-Roman Catholic Christians make a point of calling themselves catholics, and we should be sensitive to their convictions on the subject. Third--and this gets into the argument of the book--I suggest that Roman Catholics should not be so hesitant to name themselves as such, for it is turning out, at least under this Pope, that Catholicism is more fully catholic as it is less hesitantly Roman. (From the Introduction.)One might argue with that last point -- certainly it seems as if, as over the last 30+ years, the Roman Catholic Church has become more "Roman" it has become more provincial and less truly "catholic."
Even Joseph Ratzinger, in his 1961 work "Primacy, Episcopacy, and Successio Apostolica (reprinted in the 2008 work "God's Word: Scripture, Tradition, and Office" San Francisco: Ignatius Press), admits to the tension between being "Roman" and "catholic." He ultimately concludes that the "Roman" part guarantees "true catholicity." One may certainly disagree with that notion. But that's for another time.