Having a toggle would be perfect and fix the huge volume of visual clutter this currently introduces. While working on this option... allowing the colour of this line to be adjusted would also be a great option to have.
Similarly when talking to Milestones there are bugs when you allocate colours to particular Milestones. It appears the lines are more than just visual clutter they also prevent full sets data from being shown. Which means when you allocate colours to particular milestones and filter to items that were prevented from being displayed the colours go to default... change your filters back and it remembers your selection... Frustrating and a cause of tension when there is no consistency.
These are relatively simple fixes with probably multiple options for adjustment in the back end of the visual - please help us as a simple gannt like this is such an effective tool and this is so close to being very useable.