Many other scholars disagree with your unsourced statement.
And
your sources are?
And the NT writers didn't seem to have any problem remembering Caiaphas.
Let's have a look at the entirety of what these still unidentified 'writers' actually 'remembered'.
Matthew 26:57-68 (King James Version)
57And they that had laid hold on Jesus led him away to Caiaphas the high priest, where the scribes and the elders were assembled.
58But Peter followed him afar off unto the high priest's palace, and went in, and sat with the servants, to see the end.
59Now the chief priests, and elders, and all the council, sought false witness against Jesus, to put him to death;
60But found none: yea, though many false witnesses came, yet found they none. At the last came two false witnesses,
61And said, This fellow said, I am able to destroy the temple of God, and to build it in three days.
62And the high priest arose, and said unto him, Answerest thou nothing? what is it which these witness against thee?
63But Jesus held his peace, And the high priest answered and said unto him, I adjure thee by the living God, that thou tell us whether thou be the Christ, the Son of God.
64Jesus saith unto him, Thou hast said: nevertheless I say unto you, Hereafter shall ye see the Son of man sitting on the right hand of power, and coming in the clouds of heaven.
65Then the high priest rent his clothes, saying, He hath spoken blasphemy; what further need have we of witnesses? behold, now ye have heard his blasphemy.
66What think ye? They answered and said, He is guilty of death.
67Then did they spit in his face, and buffeted him; and others smote him with the palms of their hands,
68Saying, Prophesy unto us, thou Christ, Who is he that smote thee?
John 11:47-53 (King James Version)
47Then gathered the chief priests and the Pharisees a council, and said, What do we? for this man doeth many miracles.
48If we let him thus alone, all men will believe on him: and the Romans shall come and take away both our place and nation.
49And one of them, named Caiaphas, being the high priest that same year, said unto them, Ye know nothing at all,
50Nor consider that it is expedient for us, that one man should die for the people, and that the whole nation perish not.
51And this spake he not of himself: but being high priest that year, he prophesied that Jesus should die for that nation;
52And not for that nation only, but that also he should gather together in one the children of God that were scattered abroad.
53Then from that day forth they took counsel together for to put him to death.
John 18:24 (King James Version)
24Now Annas had sent him bound unto Caiaphas the high priest.
Acts 4:5-6 (King James Version)
5And it came to pass on the morrow, that their rulers, and elders, and scribes,
6And Annas the high priest, and Caiaphas, and John, and Alexander, and as many as were of the kindred of the high priest, were gathered together at Jerusalem.
That's it, DOC. The complete biblical record of (someone named) Caiaphas. Even if the people you claim actually wrote it, it's still pathetic by any measure.
How would you say this stacks up against the historical record of, say, Julius Cæsar or Alexander the Great?
What would Sir Ramsay say?