You are again engaging in giant leaps of spurious extrapolation and argument by assertion. None of the texts show apostolic succession, but what Scripture shows is only one successor being made after an apostles death, and which was by an non-political OT method Rome never has used.
After that only deacons and pastors are shown were ordained, and Paul himself was baptized by a "certain disciple," and even that "certain prophets and teachers" sent forth Barnabas and Saul for the work whereunto God called them. (Acts 13:1-3)
And that pastors Titus are those who ordained other pastors, but never those distinctively titled "priests," which is foreign to the NT, as is Rome's mass being the source and summit of Christian faith.
..and afterwards gave instructions, that when these should fall asleep, other approved men should succeed them in their ministry. We are of opinion, therefore,
Regardless of their opinion, pastors are not apostles which Rome imagine her bishops are, nor did they have the distinctive apostolic power Rome presumes even more than, as even the apostles did not presume assured infallibility of office, which novelty was not essential in order to provide and preserve Truth in Scripture.
Nowhere in the Bible does it say that we are saved by faith alone.
Wrong. Even Rome believes in baptism by desire, and contritio caritate perfecta, which can only work by faith appropriating justification by faith. And indeed, Peter confirmed souls as having their hearts purified by faith, as shown and ignored.
But what the Bible does not say is that we are saved by an inert faith, one that does not effect obedience, presuming opportunity, but remains alone, which is contrary to the faith Reformers preached.
To the contrary, I am applying common sense. Nowhere in Scripture is it stated that "Scripture alone" is the sole source of Christian knowledge. In fact the opposite is true. St. Paul says: "Therefore, brethren, stand fast; and hold the traditions which you have learned, whether by word, or by our epistle."
Furthermore, Christ, Our Divine Teacher, established a visible, hierarchical Church and directed His Apostles to "teach ye all nations; baptizing them in the name of the Father, and of the Son, and of the Holy Ghost". He instructed and directed them orally, and quite obviously, Scripture does not contain a complete record of His every word. Tradition bridges the historical gap between the life of Christ and the written Gospels. We know that the Apostles endeavored to serve the Lord faithfully and to obey His Holy Will, even unto death. Therefore, it can be quite logically inferred that the Apostolic succession is Christ's plan for His Church, communicated directly by Him to the Apostles.
The idea that Apostles, Church Fathers and early Christians would deliberately act in opposition to Christ's Holy Will by circumventing or corrupting His plans for the operation of His Church, yet at the same time submit to martyrdom rather than deny His teachings does not pass the reasonable man test.
Even Rome believes in baptism by desire, and contritio caritate perfecta, which can only work by faith appropriating justification by faith.
No, it is by grace alone that one is saved. Without grace, faith is not possible.