@JST You are absolutely correct. My apologies to all for being curt before.
A line collinear with the construction axis is needed. To do that, a plane containing the axis must be drawn using 3 point plane where 2 points are on the construction axis and arbitrary location for 3rd point. Then a line can be drawn, snapping to the axis. Finally a perpendicular construction plane added somewhere along that line. Now when the circle is drawn there is a purple dot for the center of the circle.
So now it is a couple minutes? to do an alignment operation that seems like it should be very easy.
I created a feature request here: