Furthermore the reformation gave rise to the curious idea (at least in the history of Christianity) that all is included in the Bible (or at least in the books that reformed churches recognize) and that there is nothing beyond Scripture or in addition to it that has authority. We are to accept that Jesus Christ was incarnated, lived, engaged in His ministry, suffered, was crucified, died in atonement for our sins, rose on Easter and ascended into heaven leaving behind the Paraclete, all so that a disobedient priest of eccentric views and a yen to marry a nun would be able to come along 1485 years or so later to found Jesus Christ's Church or the first of 10,000 of them, each utterly necessary to its adherents because of nuances of difference over understandings of Scripture (which is, of course, perfectly clear in its meaning despite the existence of 10,000 differing groups of Sola Scriptura believers, each his or her own authority on Scripture because most are literate and can read someone else's translation of Scripture whichever one of many differing versions or translations) authoritatively.
If you actually believe something substantially along the lines of the history outlined above, please keep it to yourself or among yourselves or go teach it to anyone who will believe it. Define your clergy as you please. I am afraid that you will find little agreement from Catholics adequately grounded in the Faith and for good reason.
Well, Peter himself wrote (I'm quoting the Catholic Bible) to "let yourselves be built into a spiritual house to be a holy priesthood to offer spiritual sacrifices acceptable to God through Jesus Christ." Hence, all believers are priests.
However, it really doesn't matter whether we agree on the definition of clergy. The Bible clearly states that deacons and bishops can be married, plus we know that more than one apostle and many, if not most, early priests and popes were married. Whether you look at scriptures or tradition, that's an inescapable fact.
Do your own research. You'll find that we know positively that Peter was married, as was Pope Felix III (483-492), Pope Hormidas (514-523), Pope Silverius (536-537), Pope Hadrian II (867-872), and others. Many others are thought to have been married as well. In fact, the Catholic Encylcopedia admits that Pope Silverius was the son of Pope Hormidas!
First of all, why do you consider this a "curious idea" in the light of Christian history? Athanasius, Cyril of Jerusalem, John Chrysostom, and Augustine all believed and argued that the scriptures were the only infallible source for discerning Christian doctrine. Check it for yourself or I'll provide you with quotes and, in most cases, linked citations. For example, in The City of God, Augustine wrote that "[God] also inspired the scripture, which is regarded as canonical and of supreme authority (emphasis mine) and to which we give credence concerning all the truths we ought to know and yet, of ourselves, are unable to learn." In his Reply to Faustus, he wrote that "in the innumerable books that have been written lately we may sometimes find the same truth as scripture, but there is not the same authority. Scripture has a sacredness peculiar to itself."
It sounds to me like if Augustine were on this thread he would be arguing forcefully for sola scriptura! I don't know where you get the idea that considering scripture as the final authority just appeared out of nowhere some 500 years ago. In actuality, you ought to be asking yourself why the doctrine was held by the early church, then managed to get lost in the Dark Ages until Luther resurrected it.
I think that you are operating under a misunderstanding of what sola scriptura really is. I'm not against tradition and neither are most Protestants. Sola scriptura simply means that scripture is the final arbiter of doctrine. We can use tradition, the writings of others, and even secular history to illuminate scritpures, but if a tradition violates the clear meaning of scripture, then it must be tossed out. The early church called scriptures the canon, which means a measuring rod. The name was no accident as the early church absolutely considered it the standard by which all doctrine is to be judged. Somehow along the way that idea became lost.
Next, look in your Bible and see how often Jesus and the apostles appealed to scripture as the final rule. The words "it is written" appear around 90 times! Jesus appeals to scripture 3 times in his dispute with Satan. Jesus didn't have to do that because he could appeal to his own authority. However, he appealed to scripture in order to teach us how to do the same. Jesus rebuked the pharisees in Matthew 15 for "[nullifying] the Word of God for the sake of [their] tradition." Paul warns us in 1 Corinthians to "not go beyond what is written."
Further, take a look at how many times in the Sermon on the Mount Jesus confronted what the Jewish leaders of the day said and contrasted to what is written in the scriptures. Remember that the Jewish leaders of the day had their own doctrine of infallibility and had a habit of piling on traditions that had no scriptural basis.
Jesus said in Matthew 22: "You do err in not knowing the scriptures." That's a good rule to go by.
I assume that you were using hyperbole because that's a gross overestimation of the number of Protestant churches. My point though is that the Catholic church is just as splintered as Protestant churches. The Franciscans, Jesuits, etc. are no more closer together or further apart than, say, Baptists and Pentecostals. Go to a Hispanic Catholic church in a southwestern state and, I promise, you'll be shocked. Most of them are one part Christianity and two parts indigenous Latin American folk religion. The priests garner the same kind and amount of respect as the local bruja or curandero. Just because a church is called Catholic doesn't mean that it's in lockstep with Rome. We won't even talk about the divergence from traditional beliefs held by liberal Protestant and liberal Catholic churches!