Hello,
Im desiging a 3d printer from scratch and Im wondering why direct extruders' motors are geared down so much and bowden are not? What if I took a bowden extruder and mounted it directly on the printhead? Would print quality be much worse?

I don't see much correlation between bowden/direct and ungeared/geared. I can say, however, that geared extruders are generally more precise and have more torque, but also more complicated and less reliable. Most people seem to like geared extruders, but I've been using a direct-drive Bowden for a while and I've loved it.

From what I've been reading lately, it seems that 3:1 gearing is the optimum balance between weight, torque and fast retraction. You need more retraction for Bowden so having a direct drive will allow that retraction to happen faster, but if it's ungeared you'll need a higher torque stepper motor to produce the same force on the filament. If you want to mount it on the print head, you need to keep the weight down so a smaller motor with gearing will probably be lighter than a larger motor without. Take your pick.

Thank you for your advice, i will reconsider that