Actually, it’s just the facts that the Baptist movement arose out of Anabaptists in the 1600s, and the Anabaptists arose out of the Anglicans.
I’ve read some works in the past that suggest the Anabaptist link is weak but I certainly agree with you that it is preposterous to claim an unbroken chain from the apostles to Baptists.
Since faith and regeneration are the gifts of God, we don’t need to prove unbroken apostolic succession. It’s not necessary. The faith of the apostles is what matters, not traditions. Only God can give that.