Thinking about different types of extruder designs, and especially remote direct drive, I wondered if anyone's ever made a cartesian bed slinger printer (Ender 3 style) where a direct drive extruder on top of the X carriage is driven by a stationary E motor at the end of the gantry via a belt. This would of course turn the extruder hob whenever there's motion along the X axis, so the X and E motors would have to be synchronized, with effective extrusion being the difference of the X and E motor motions (thus my allusion to CoreXY in the name). Are there reasons not to do this, aside from needing an over-engineered belt assembly with closed loop belt? It seems like you could get whatever reduction you need just with an appropriate belt pulley, and no need for a gearbox on top of the hotend to get the necessary torque to the extruder hob.
Of course as described this only makes sense for bed slinger printers, since if you have to move the gantry in the Y direction, you have the motor mass moving just like a normal direct drive. Of course it might be extensible to "CoreXYE" with an appropriate belt layout.