There are a few reason why the tapered hole requires so much time and attention.
First it is the tapered mortise and tenon joint, with the wedge to lock it in place, that makes the Windsor chair so strong. If improperly tapered and assembled the joint and thus the chair will actually work itself apart so the chair actually pulls itself to pieces. If assembled properly, however, will last forever.
The second reason these joints are important is that they directly determine the angle at which the legs hit the floor. When looking at a chair from the front this angle is called the splay and when from the side, rake. If these angles are different for each leg then we can still make all four legs touch the ground but the chair will look lopsided and a seated person will put uneven pressure on the legs.
Not too many photos of the process but this one gives the idea. The reamer (the t shaped tool under Pete's elbow sticking out of the seat) is lined up simultaneously with the square (in the middle) and the bevel gauge (on the left).
Next we carved our seats. The goal is to make one fluid curve that will support the sitters weight in the most natural way. If your run your hands from front to back of the bowl you do not want to feel any distinct transition.
Finally, I spent some time at lunch and during a break tuning up a drawknife that belonged to my grandfather. Hopefully I'll be able to use it for the next chair I make.
This is the before shot. An after shot in due time.