Do you mean strongly Catholic by membership (i.e. baptism)? In that case there are several countries in the world today which ARE 'strongly Catholic.
Or do you mean strongly Catholic by practice of Catholic doctrine, dogma, and discipline? If so. . .well, to paraphrase G.K. Chesterton, ‘it’s never been tried’. And in the times it had been (Europe circa approximately AD 400 to AD 1600) the countries had to fight Muslim conquest attempts, barbarian invasions from all points of the globe, heresies, war, famine, natural disasters, etc. so that even when things in a given country might have been more or less stable, the government could go loopy, there could be wars among the nobles, or a hedge priest could decide to do an Albigensian kind of thing. Even so, the average person’s faith may not have been as privileged as ours, what with our longer life spans, free men (and women), literacy, etc., but from the records we have and the literature etc it appears that what people did have was stronger and more heart-felt. We have more ‘power’ now and we all know power corrupts and all that, so maybe the balance needs to be worked on. . .