The four turned finials on this chair are not simply ornaments stuck on the corners - they are the tops of the actual corner posts, and that is why they look right.
A finial applied to the end of a post always shows a joint line, and once a viewer has seen that line the finial reads as an addition. So the corner posts here are made from stock long enough to include the finial, and the finial is turned from the same continuous piece of timber as the post beneath it.
The turning is done before the post is carved and jointed into the chair, on a lathe, with the plain shaft left oversized so the post can be worked square-to-round afterwards.
It costs more timber - the stock has to be thick enough for the widest part of the finial along its whole length, most of which is then cut away. That waste is the price of a finial that grows out of the post rather than sitting on it, and on a chair whose whole effect depends on verticals, it is worth paying.