I don't know about "twitchiness," although I've heard the word used to describe track bikes on the street.

I know my Bianchi Pista feels stable at the highest speeds I can hit with it, probably well short of 30mph.

My Pista also feels wonderful at very, very slow speeds.

And then, at normal cruising speeds (19-20mph for me), it seems to pick its way through the road debris without any conscious effort on my part.
I also note I can "throw" the front wheel sideways, although I know the wheel stays in contact with the road.

All of this said, I would never think of taking my hands off my Pista's handlebars.

Someone brought up weight distribution, or what I would call Center of Gravity.

A bike has a center of gravity around the rolling or leaning axis, but it also has a center of gravity around the yaw, or turning axis.

I have a 35mm setback seatpost, and this puts me further back over the rear wheel than most folks.
I wonder how this changes things.