Interesting thoughts. Although it would seem that since many of North America's first European settlers were escaping state mandated religion, perhaps the Catholic church's impact in establishing a separation between the church and the state might not have buried its roots too deeply in Europe. Furthermore, Spanish Conquistador's working for both the state and the Catholic church were not especially interested in the "worth of individuals" as "free moral agents", but I guess that depends on how one defines the word "human". Really, I wasn't aware the concept got much press until Thomas Jefferson wrote the Declaration of Independence, but maybe I ought to read Weigel's book.
There is a difference between establishmentarian (there, I have finally used that word!) religion and denying the state's authority in ecclesial matters. One may establish a given religion as the only legal one in a nation and yet still have an independent ecclesial structure. In pre-Reformation England, for example, an abbot enjoyed broad rights within his monastic domain, derived naturally and necessarily from his ecclesial rights, that often frustrated civil authority. This is one of the reasons Henry VIII had mostly to destroy the monastic system in his realm: it fundamentally interfered with subjugating the Church to his own political goals.
In this sense, one might understand your statement perhaps the Catholic church's impact in establishing a separation between the church and the state might not have buried its roots too deeply in Europe is actually the opposite of the facts, since it was English settlers who emigrated from England to escape the established church, created by Henry VIII when he destroyed the Church's independence from the state!
French, Irish, and Spanish settlers retained their Catholicism, by and large, in new lands, so their emigration from their homelands was motivated by something other than escape from homeland established religions. Perhaps Protestantism's tendency to create myriad sects, often maliciously intolerant of each other (I do not deny Catholic guilt in this respect toward nonCatholics, in the past, mind you), might be the cause of English emigration and motivation for a constitutional establishment clause. But the moral force qualifying individual self-dignity as an important component of liberty cannot be found, I assert, in civil traditions. That comes from ecclesial teachings, and only a Church that has thrown off imperial, regal, or statist attempts to regulate it can adequately express such ideas. A state-controlled church will suppress individual liberty when required to do so by state politics and policy.
It just may be, ironically, that innoculated with the idea that the state must not be the all in all for humanity by the history of the Catholic Church, men grew Protestantism into a philosophy of liberty that resulted in civil liberties unknown in any culture before. We must hope that liberty does not become libertinism and work to retain Christian roots that admit Authority that is not statist, but which disciplines liberty.
Regards.