No, not surprising. Rather, it is typical. little is known of the lives of any of the so-called "unbroken line of Popes" for hundreds of years. Some cynics may even call it a fictional list. (sarc)
Clement was the Bishop of Rome with no "supremency" over the other Bishops. There was no such title as POPE!
That is true, the word Papa is of a later origin, and it was originally a term of endearment. The formal title is Bishop of Rome to this day. St Clement wrote his Letter to the Corinthians to instruct the Church in Corinth regarding some defrocked priests. That was far from Roman local jurisdiction.
Clements' letter was of a pastoral nature and certainly did not illustrate anything resembling a universal "Supreme Pontiff".
"If anyone therefore shall say that blessed Peter the Apostle was not appointed the prince of all the apostles and the visible head of the whole church militant or that the same directly and immediately received from our Lord Jesus Christ a primacy of honor only and not of true and proper jurisdiction, let him be anathema."
An old song, but it never loses its charm, does it?
Of most others we know plenty detail and their works survived. Linus, most likely, was killed quickly as were most early popes.
Clements' letter was of a pastoral nature
Yeah, right. Here's a sample:
You therefore, who laid the foundation of this sedition, submit yourselves to the presbyters, and receive correction so as to repent, bending the knees of your hearts. Learn to be subject, laying aside the proud and arrogant self-confidence of your tongue. For it is better for you that you should occupy a humble but honourable place in the flock of Christ, than that, being highly exalted, you should be cast out from the hope of His people (57)yield submission to His all-holy and glorious name, that we may stay our trust upon the most hallowed name of His majesty. Receive our counsel, and you shall be without repentance. (58)
If, however, any shall disobey the words spoken by Him through us, let them know that they will involve themselves in transgression and serious danger; but we shall be innocent of this sin (59)
submit the neck and fulfil the part of obedience, in order that, undisturbed by vain sedition, we may attain unto the goal set before us in truth wholly free from blame (63)
Send back speedily to us in peace and with joy these our messengers to you: Claudius Ephebus and Valerius Bito, with Fortunatus; that they may the sooner announce to us the peace and harmony we so earnestly desire and long for [among you], and that we may the more quickly rejoice over the good order re-established among you. (65)