I only asked why it terminated at the centre of the valve socket and why the corresponding tab that it shares a relationship with was empty.
... That center pin is very useful in RF circuits but really has no application at audio frequencies.
SEL49 gave you the answer, but more explanation might have helped.
A "capacitor" is just a couple of conductors separated by an insulator. So if you look at the socket-pins, you might observe there is capacitance between the different pins.
You can find the formula that explains how the parts of the capacitor influence capacitance, but suffice to say the socket's pins have a
very small capacitance between them. Too small really to imagine a "phantom cap" connecting the pins at audio frequencies, but at
radio frequencies... Here, it turns out the capacitance is big enough to matter for RF circuits.
How to combat unwanted phantom-capacitor connections at RF? That center-spigot splits the distance between pins across the socket from each other in half. 2 capacitors in-series create an even smaller total capacitance, which would move the affected frequencies higher.
Except socket-manufacturers gave another, better option: Ground the spigot, either directly or by
using a connected tab as a wire tie-point. Although we could envision 2 cross-socket "phantom caps" in-series, we can instead imagine a cap-to-ground from "pin to center-spigot" that prevents signal on one pin from being coupled into another pin where it doesn't belong.
Tube manufacturers eventually considered the end-user's possible use of sockets with these center-spigots, and also possible coupling among tube-pins when they
design the tube and decide what-circuit-element will be brought out to what-pin, and what that implies for unwanted coupling and end-user circuit-wiring.