One thing that is certain is that any claimants to Christianity through physical succession cannot be acceptable to the church. Every NT letter writer except James warned strongly of the existence, incipient, if not actually present among Christians as they wrote, of false brethren. Paul warned the bishops of Ephesus that, after his departure, 'grievous wolves' would arise from among 'your own number'! So even if a teacher starts off in true faith, it does not mean that he will stay faithful. Bribery or persecution can easily turn a man from the straight and narrow. To claim succession from 'wolves' is of course disastrous, but these men that 'Tradition' people follow could have been the very sort of people that Paul warned of. 'Tradition' people don't know that they were not, and they cannot be truthful if they claim to know that they were not, and cannot be accepted into the church.
In fact, the traditions of man since the apostles left this world have in every case been akin to those of the Pharisees- outward show disguising inward disobedience and corruption, easy versions of tough truths. Real succession is doing as only Jesus and the apostles commanded, nothing more, nothing less. Protestants find that hard, too, but again, Christians do not associate with any who condone failure to do so.