I've tried it and there is still a problem: the cursors draw from wherever the previous cursor was. This makes it impossible to draw a line of cursors verticall

I've tried it and there is still a problem: the cursors draw from wherever the previous cursor was. This makes it impossible to draw a line of cursors vertically through your text without first placing a single cursor at either the top of the bottom of where you want to draw the line. So instead of click-drag (with a modifier key) you have to click-click-drag (with a modifier key).