You could probably get better answers from the company you name, that may have a history going back a hundred years or so, or maybe also numerous other companies such as Rockwell/Smith-Blair, Romac, Ford, JCM, Victaulic/Brico etc. or many other international folks that I believe may presently also market couplings very similar in principal to those made by Dresser for much of the last century. I guess they might say that unlike welded joints the couplings can of course basically be assembled rather quickly with simple small wrenches, in virtually any weather or conditions, and of course maybe also without as much need for welding equipment or expertise etc. Also unlike welded joints, the couplings are capable of providing some significant level of deflection, or corrections to alignment etc. (in the case of imperfect surveying or construction etc.), and even after assembly due to settlement or seismic etc., essentially without bending or imparting bending stress or heat to pipes/linings/coatings etc. It is even possible some serviceable joints might perhaps be made with lesser specific control of radial alignment between pipe ends than is necessary for the best quality welds. I even suspect well-assembled coupling joints might even allow some level of axial movement, or rebating axial movement, between pipe ends, though I would think this could be some limited (in magnitude/cycles etc.) due to the still rather labor intensive and labor-reliant as well as highly confined nature of the stuffing-box seal and pipe end surface conditions etc., again without stressing the pipes.
Some of these same features that make the couplings desirable might arguably also be detriments in some applications, particularly when the joining concepts and limitations are not well understood. For example, such stuffing-box couplings in and of themselves, unlike a weld, are not restrained joints, and if the pipes are subjected to forces attempting to overdeflect or pull the joints apart, there is nothing in the coupling itself that will prevent this (supplementary restraint can however be provided with rods/harnesses etc.)
Likewise, the couplings normally employ some sort of rubber or elastomeric seal with perhaps far different properties (including heat, hydrocarbon from inside or ouside the joint, or other resistances etc.?) than the normal steel of some process piping etc. Again, if not well understood, and particularly when not judiciously chosen and assembled properly for the exposures, this can eventually result in problems.
Finally, although not requiring a skilled welder the bolting of the couplings is however some labor-intensive and reliant, and may in larger sizes require proper lubrication and several even, circumnavigations of tightening around the joints to appropriate torque levels. If this sometimes hard work, particularly in larger pipe sizes that have a great many bolts, is not completed with adequate knowledge and diligence, problems(leaks) can also result. Of course, however, there can be various problems with fused or welded joints as well!
Maybe this brief discussion will at least provoke more detailed and/or learned responses.