if you make it rigid then your alignment needs to be absolutely perfect and you need to 'clock' the shafts to each other first by putting a DTI on one shaft and rotating it around the other in several places to ensure it is both parallel and concentric. This is not an easy task if your coupling lives hidden inside a bellhousing and even harder if you don't have a shimming/adjustment system. The jaw couplings allow easy assembly plus have a stated acceptable misalignment amount. Any misalignment in the shaft that is forced into alignment by tightening a rigid coupling will cause extra stresses and lead to something failing.