You bring up a good point and it's something else I've been wanting to elaborate on. It's a bit lengthy. To any Catholics reading, I want to point out that I am NOT arguing for this view here... that is not what I do. Instead, I am simply pointing out the way some of us Protestants see things.
Most Protestants recite the Nicene Creed during our worship services. Everything within that Creed is an essential part of our faith, and that includes the reference to the "One holy catholic and apostolic Church." Our interpretation just happens to be very different than that held by Catholics.
Catholics have been known to throw out the, How Old Is Your Church argument when debating with Catholics (I've seen it at least twice in this thread alone). While factually correct in its assessments regarding the ages of particular church bodies, it is a poor example of apologetics as it completely ignores the Protestant understanding of the Church to the point of being irrelevant.
Protestants don't identify "The Holy Catholic and Apostolic Church of Christ" with any particular earthly institution. We see earthly Churches as being human institutions composed of men. Many of us will grant that the institution now known as The Catholic Church was technically founded by Christ since it grew out of that original body of believers commissioned by Christ. Whereas Catholics believe that this particular institution is synonymous with the entirety of the universal Christian Church, however, Protestants distinguish between the two. We believe that Christ founded a spiritual body, not a structured institution, and that while the latter certainly characterized the former in its early years it is not necessarily an essential property.
Our view, then, is that in early Christianity the universal Christian Church was synonymous with what Catholics would call the Early Catholic Church. Defined doctrine was not monolithic within that body - Protestants would argue that beliefs which characterize our beliefs existed alongside doctrines which are more characteristic of the Catholic Church today. It is easy to forget that things were not as clearly defined back then as they are now, particularly in terms of salvation by faith and Scripture as the as the ultimate measure of Tradition. If I am not mistaken, where doctrine has not been explicitly defined in the Catholic Church there is freedom of opinion.
Unfortunately, the hardness of hearts in men led to splits in the institutional structure of the Church. From a Protestant point of view, where one Institutional Church once stood, after 1054 there were two Institutional Churches (or perhaps even more, if you include groups like the Coptics, whose schisms might have been due more to a misunderstanding than actual heresy). The universal Church itself was not split in twain according to the Protestant view, but merely the institutional administrative bodies that ministered to the members of that Church.
With the Reformation, what Protestants perceive is not the creation of a bunch of new Churches so much as a mass of organizational schisms which led to new administrative institutions based around differing points of view. Considering that we do not believe institutional unity to be a necessity, we are quite alright with this. At this point it is essential to define what Sola Scriptura really is. To the majority of Protestants, Sola Scriptura does NOT mean that all doctrine must be DERIVED directly from Scripture. That is not the classical understanding. Instead, the doctrine derives from the idea that Scripture is the inspired and infallible Word of God. Doctrine, forms of worship, the actual canon - these things all undeniably preferably proceed from Tradition going back to the time of the apostles. What Sola Scriptura teaches, however, is that Tradition must be weighed and measured according to what is taught by Scripture. Traditions which are not taught in Scripture are held not to be necessary for Christian salvation. The application of this is different depending on denomination, of course - some, like myself, see non-scriptural traditions as perhaps good yet non-binding while others believe that traditions not affirmed by Scripture are to be outright rejected. Other differences arose regarding methods of interpretation. Yes, new understandings of Christian doctrine inevitably arose and new denominations were founded around those, but these were considered much along the lines of "Development of Doctrine" within new contexts rather than sudden discoveries of "Real Christianity." Among Protestants, "Real Christianity" is pretty much the same as it is among Catholics - Faith in Christ as Lord and Savior. The differences are in forms of worship and in particular doctrines that are ultimately considered non-essential to salvation.
It is essential to understand that, within the Protestant view, the "one holy catholic and apostolic Church" is not identifiable with one institution and is intangible here upon earth. As an Anglican, I accept that my Church has no claim to representing the ENTIRE Church of Christ, which I hold to include Catholics, Orthodox, Lutherans, Presbyterians, Baptists, and a host of others. Outside the Church there is NO salvation, but all Christians ultimately belong to it. This is not to say that the Church is "invisible" by any stretch, however - it is very visible through the various institutional organizations that represent it! It's "unity" consists of our willingness to place aside doctrinal differences in love and charity and focus upon our similarity - our Faith in Christ.
Agree, disagree, whatever... I just wanted to share some of my views on the "Church" subject.
From OUR POV, Your mileage may vary (and it looks like it does) ;-)
The "invisible church" idea is only necessary after there have been organizational splits. With different organizations sort of dealing with each other with uplifted noses and at arms' length, then there is a need for some account of the sort of big old Church and these itty bitty churches. And for Protestants, of course, that account cannot include any serious pre-eminence for the Holy See and those in actual communion therewith.
Our (arrogant - you be the judge) way of dealing with it is to say that there is one Church. So all the Baptized are in it, though some are not such good members or not so far in. (We have to allow for really awful full fledged Catholics and Spirit-filled Protestants -- the first being impossible to deny and the second being eagerly affirmed, at least these days.)
A Protestant recently argued in favor of the KJV and the "textus receptus" that God providentially preserved a stream of texts and translations from error. We make the analogous claim about the Church. Despite the incredible lack of organization and intentionality which, despite its reputation, really characterizes the Catholic Church, despite the dreadful scoundrels and buffoons, despite the worldly cynicism of some clerics and the perversion of others, the Church is, we think, preserved free from error -- where it really counts.
We see this preservation as an unmerited gift from God, as an example of His persistent faithfulness in the face of our remarkable contempt for Him.
The one advantage we might claim for this point of view is that if you want to have access to bona fide sacraments, go to a Catholic Church, whether Roman catholic, Byszantine, Maronite ... any church in communion with the Holy See. And, we think, if you want bona fide, reliable teaching, then enter the conversation with the magisterium. We think you don't have to guess or to sample this or that denomination.
I'd even say, I HAVE said, if your priest is a jerk, don't worry. The sacraments are still real, and you can go to Scripture and the Fathers and the Catechism for reliable teaching.
Another kind of philosophical advantage, or at least feature, is that our doctrine does not gnosticize or Platonize the "real" Church. It is here, warts and all. YOu can't always tell the good and reliable members, you won't know if you have confused wheat with tares in the individuals you encounter. But it's right here, as Moses says about the Torah.
This also was not meant to be persuasive or polemical but rather expository, and I hope it was useful.