One of my pet peeves about my 06 XJ8 L is that the throttle response is (to my view) overly aggressive from a standing start. Very difficult to take off smoothly from a stop sign without a jackrabbit start or even tire spinning. Not noticeable once underway, at road speeds. Is this a bug or a feature?

Sticky throttle butterfly or TPS?
Just some ideas

Tyres (inflation/size/type/brand/etc) or suspension may be part of the cause.

Yep; first thing I'd look at. I had the problem years ... well, decades ... ago on a car when the throttle cable was badly worn.

And if not the TPS then possibly the actuator motor on the throttle body could be getting a bit erratic.I know since I replaced my throttle body stepping on the pedal is more responsive and the slight stumble coming to a stop is gone.

I know exactly of the issue you describe, as my 05 XJR has it too.
the initial throttle sensitivity is very high on these cars it seems. I know that you can 'recalibrate' your throttle pedal after you remove the battery terminals. It requires putting ignition to "II" and slowly depressing the throttle all the way down and back 3 times.

Im sure an aging throttle body motor makes this issue worse too.