It seems like the non-Catholic bible believing churches have no more use for the Apostles if they believe that all they need is in the bible. They have their source of truth in their scriptures and it seems like that has replaced the Apostles and their preaching as the defined truth.
Protestants also don’t have apostolic succession the same way that we do. Some denominations still practice something resembling it, but none are considered valid by the Catholic Church as far as I’m aware.
With that said, traditional Protestantism does at least recognize “apostolic teaching”, that being the teachings found in Scripture. To them, the “apostolic church”, as mentioned in the Nicene Creed, would be whatever carries on this teaching. Sure this may not be the historical way of viewing it, but it’s out there as a way of staying “apostolic”, as the Nicene Creed demands, while not demanding an authority like that of the Catholic Church or Eastern Orthodox.
This would also mean that they don’t need any understanding of early Church Fathers writings to corroborate any doctrine or issue in the faith.
Traditionally, Protestants still respected Tradition, even if they felt that it was theirs to pick and choose as they saw fit (to paraphrase John Calvin). It’s why most Protestants, particularly the more traditionally-minded ones, will still revere the Apostles Creed, Nicene Creed, Athanasian Creed, etc.
When I was a Presbyterian, we understood tradition as being an interpretation of Scripture that had the benefit of coming from someone very close to the time of the Apostles and therefore likely to better understand the context and meaning. They were fallible but valuable, some without error as we understood it.
That said, many Protestants are OK submitting to fallible authorities without question, but that’s a whole other discussion.
It also means there is no magisterium or continuing liturgical priesthood and the seat of Moses has ended.
Yes, and Protestants don’t care.
They have traditions, whether they admit to it or not.
When I was a Presbyterian, us and Lutherans would sometimes joke that “No creed but the Bible” is itself a creed and therefore impossible to hold to.