Yes, I meant the trebuchet. Way to cumbersome to be dragged along, I agree.
From what I gather most big caliber siegeweapons in medieval times was assembled on the spot using local timber, which was still in abundance in medival times.
Of course the most effective siege method was digging a cave under one of the city walls. Placing timber buttresses in the cave under walls could withstand the pressure form above, while the workers dug away. So all that had to be done was to grease the supporting burtresses with tar and then put them to the fire and the walls would collapse.
Rome: Total War did put some effort into representing the art of siege warfare, but I have yet to see a game that presents the full science of breaking a fortification.
In the 17th century siege warfare would get so complex that a siege could be won without firing a single shot.
The garrison would simply surrender, once the trenchdiggers managed to dig themselves close enough to the fortification to set off a powderkeg that would blow the whole thing up.
It would be cool if somehow workers could be involved in siegewarfare. I.e. order the workers to make an "improvement" next to the besieged city that would dramatically lower the defense bonuse of the city.