With a little review, allow me to be more careful. Compasses are assumed to collapse for classical constructions, as this is the assumption made by ancient Greeks (and they kinda started this :-) ). From what I can tell, Euclid showed in his 2nd proposition (Elements) that with a straight edge, the two types of compasses are equivalent, and I have seen a simpler proof that doesn't require the straight edge. So the assumption is merely inefficient in this case.

However, if those interested in construction efficiency under different assumptions, it becomes important. (I know, that isn't what is being asked here.)

On a side note, I can confirm that being able to mark a single distance on the straight edge allows for a fairly short construction for trisecting an angle. There is a fairly dicey lining up of three points that goes beyond the two point game we are used to playing with a straight edge. Neat stuff!