I too have learnt something today.
My first thought whan I saw the post was, why would anyone want to use a taper spindle? a conventional parallel spindle looks the obvious solution. Having followed the link I now know that a taper spindle is absolutely normal for a clapper box. I can imagine a variation of the idea using shims to change the axial relationship of the two parts to eliminate the need to have a reamer whan adjustment is required.
I would have though that a clapper box bearing arrangement would not be in the least critical. In use any backlash or play would be taken up the moment the cutter tip hits the job. The clapper box will be pushed back against whatever stop it has, and as long as it hits the same stop every cut, the cutter tip will sit in the same place for every stroke.
My curiosity is aroused now ! if a taper pin in tapered hole makes such a good spindle, why isn't the technique in much more common usage?
Ian