That simply is not true. We simply do not know what happened in the churches from around 70 AD to 120 AD. We have no knowledge that the gospels as we know them were received and recognized. We don't know who touched them and what changes were made.
Considering Matthew, Mark, Luke and several of Paul's epistles were quoted through the end of the 1st century and exponentially into the 2nd century, I don't see how your statement holds water.
The quoted books are: Mt, Mk, Lk, Acts, Rom, 1 Cor, 2 Cor, Galatians, Ephesians, 1 Thessalonians, 2 Thessalonians, 1 Timothy, 2 Timothy, Titus, Hebrews, James, 1 Peter, 1 John, Revelation
Here are the rest of the quotes:
Clement of Rome (96-98 A.D.) quotes Matthew 18:6 (also Mark 9:42) as by the Lord Jesus Christ.
1 Clement ch.46 p.17-18
Letter of Polycarp to the Philippians ch.2 p.33 (110-155 A.D.) quotes all of Matthew 7:1 "but be mindful of what the Lord said in His teaching: ‘Judge not, that ye be not judged;"
Clement of Rome (96-98 A.D.) quotes Mark 7:6 1 (Also Matthew 15:8; Isaiah 29:13)
1 Clement ch.15 vol.1 p.9
Polycarp (100-155 A.D.) quotes Luke 6:36
Polycarp’s Letter to the Philippians ch.2 p.33
Clement of Rome (96-98 A.D.) quotes 1/4 of Acts 20:35f (5 words out of 26 words)
1 Clement vol.1 ch.2 p.5
Polycarp (100-155 A.D.) quotes half of Acts 2:24a (7 out of 15 Greek words)
Polycarp’s Letter to the Philippians ch.1 p.33
Clement of Rome (96-98 A.D.) quotes Romans 1:32b
1 Clementch.35 p.14
Clement of Rome (96-98 A.D.) quotes 1 Corinthians 2:9
1 Clement ch.34 p.14
Polycarp (100-155 A.D.) quotes one-fourth of Galatians 6:7 "God is not mocked" (3 out of 14 Greek words)
Polycarp’s Letter to the Philippians ch.5 p.34
Ignatius: Paul wrote a letter to the Ephesians according to
Ignatius’ Letter to the Ephesians ch.12 p.55
Polycarp (100-155 A.D.) quotes Ephesians 4:26 "For I trust that ye are well versed in the Sacred Scriptures, …It is declared then in these Scriptures, ‘Be ye angry, and sin not,’ and , ‘Let not the sun go down upon your wrath.’" (12/12 words of the verse)
Polycarp’s Letter to the Philippians ch.12 p.35
Ignatius quotes 1 Thessalonians 5:17 Ignatius’
Letter to Polycarp ch.1 p.93
Polycarp (100-155 A.D.) quotes half of 2 Thessalonians 3:15a (5 out of 9 Greek words)
Polycarp’s Letter to the Philippians ch.11 p.35
Ignatius quotes one-fourth of 1 Timothy 1:1 "Jesus Christ who is our hope"
Ignatius’ Letter to the Magnesians ch.1 p.64
Polycarp (100-155 A.D.) quotes 1 Timothy 6:7 "Knowing, therefore, that ‘as we brought nothing into the world, so we can carry nothing out,’ (11 out of 12 words)
Polycarp’s Letter to the Philippians ch.4 p.34
Polycarp (100-155 A.D.) quotes half of 1 Timothy 6:10a. "But the love of money is the root of all evils." (8 out of 21 words)
Polycarp’s Letter to the Philippians ch.4 p.34
Polycarp: (100-155 A.D.) quotes 2 Timothy 2:12 He [the Lord] has promised to us that He will raise us again from the dead, and that if we live worthily of Him, ‘we shall also reign together with Him,’ provided only we believe."
Polycarp’s Letter to the Philippians ch.5 p.34
Clement of Rome (96-98 A.D.) quotes half of Titus 3:1b "Ye never grudged any act of kindness, being ‘ready to every good work.’ (6 out of 13 words)
1 Clement ch.2 vol.1 p.5
Clement of Rome (96-98 A.D.) quotes Heb 1:4. "’who being the brightness of His majesty, is by so much greater than the angels, as He hath by inheritance obtained a more excellent name than they.’ For it is thus written, ‘Who maketh His angels spirits, and His ministers a flame of fire.’ But concerning His Son the Lord spoke thus: ‘thou are my Son, to-day have I begotten Thee. As of Me, and I will give Thee the heathen for Thine inheritance, and the uttermost parts of the earth for Thy possession.’ And again He said to Him, ‘site thou at Mu right hand, until I make Thine enemies thy footstool.’"
1 Clement ch.36 vol.1 p.15
Clement of Rome (96-98 A.D.) quotes half of Heb 3:2b
1 Clement ch.17 vol.1 p.10
Clement of Rome (96-98 A.D.) quotes three-fourths of Heb 10:37
1 Clement ch.23 vol.1 p.11
Clement of Rome (96-98 A.D.) quotes James 4:6 (same as 1 Peter 5:5b; Proverbs 3:34)
1 Clement ch.30 vol.1 p.13
Polycarp (110-155 A.D.) quotes all of 1 Peter 2:22 in
Letter to the Philippians ch.8 p.35.
Polycarp (110-155 A.D.) quotes the first half of 1 Peter 3:9.
Letter to the Philippians ch.2 p.33. He also quotes the last fourth of 1 Peter 1:11 in ch.5 p.34. He quotes the first half of 1 Peter 2:23 in ch.8 p.35
Polycarp (100-155 A.D.) quotes half of 1 John 4:3a,c (13 out of 34 Greek words, with gaps)
Polycarp’s Letter to the Philippiansch.7 p.34
Clement of Rome (96-98 A.D.) quotes: Revelation 22:12 p.14 (This is also the same as Isaiah 40:10; 62:11)
1 Clement ch.34 vol.1 p.14