In my eyes, the identification of "Protestant" is a silly one. Because "Protestant" basically means non-Catholic, it can be broadly applied to a wide range of beliefs, from true beliefs like Sola Scriptura and Sola Fide, all the way to outright wacky beliefs such as the "Prosperity Gospel".
Because of this, Catholics are able to capitalise on living straw men, presenting the teachings of one "Protestant" denomination as general "Protestant" doctrine, when in reality, there are far too many "Protestant" beliefs for any one argument to suffice as a refutation.
Catholics actually know this, as is demonstrated by the fact they have an equal and opposite argument. Citing anywhere from 30-60,000 "Protestant" denominations (with even the minimum being greatly exaggerated), Catholics also argue that the Church is divided when it divides from the Catholic Church. The solution? Come "home" to Rome.
Due entirely to human ignorance, Catholic apologists tend to argue both ways, and Catholics don't recognise the contradiction. In reality, "Protestants" can answer both using one consistent flow of reasoning. In fact, the simplest way I like to put it is that "Protestants" disagree on the Bible for the same reason Catholics disagree with the Bible.
To elaborate on that a little, consider the way a Catholic reads the Bible vs. how a "blank slate" reads the Bible. Of course, in reality, no one is truly a blank slate, but for sake of argument, let's imagine an agnostic walks into a book shop and purchases a Bible. What's he going to do when he takes it home? He's just going to start at page 1, maybe get bored when it comes to genealogies and shelve it for a bit, but ultimately, he's going to read it like any other book. When he does so, will he have a clue what Catholics believe?
Studying scripture is often enough to make people leave the Catholic faith. Catholics, to this day, aggressively oppose private Bible study, even claiming it is arrogant to believe you can do so. "You won't find anything no one has found before". "Imagine thinking you know more than the Church Fathers". "You make yourself Pope". This is ignoring the Catholic Church's historical opposition to translation and private ownership of scripture.
The fact is, the Bible is just not a Catholic book. You won't find the Marian dogmas, the Papacy, a special class of priests, Purgatory, or any Catholic traditions in the Bible. So why do Catholics believe them? Precisely because of that tradition! If a Catholic believes in their tradition, the Bible does not need to present, or even support it, they will believe it, and if necessary, the Bible will be made to support it. But they are not alone in this! Many "Protestants" do it too, whether it's to support whatever remnants of Catholicism that particular "Protestant" denomination may retain, or some entirely different belief.
The irony is, even joining the Catholic Church, completely surrendering your right and ability to read, would not solve this problem, because Catholicism is divided internally, too. At every level, from Pope to commoner, Catholics have different beliefs. At the end of the day, the problem isn't the clarity or sufficiency of scripture, the fallibility of the Pope, or the authority of the Magisterium. The problem is an entirely human one. When mankind neglects to love scripture, they are doomed to fall into a number of errors. The solution? Love the scriptures!
One thing Catholicism has in common with Christianity is its teaching that the 66 books of scripture are the word of the living God. Conveniently, that same word claims to give understanding to the simple, and that those who delight in it, frequently meditating on it, will gain great understanding. For this reason, I issue a simple challenge to Catholics: Read Psalm 119 twice over, once with the mentality of a Catholic, and once just as it is written. Soon, you will see that not only can scripture be understood without the aid of tradition, but it is actually heresy to say otherwise. Therefore, it is illogical to paint all "Protestants" with the same brush, but it is also illogical to argue that since so many "Protestants" depart from scripture as egregiously as Catholicism, therefore scripture itself is in some way deficient. In the end, the Bible is the word of God, as we all agree, and therefore, it is essential that we treat it as such.