Everyone will tell you they understand the hazards and seek a more effective paradigm. Actually, the synonym is sequential process (sounds better, and more sophisticated) and the better idea, practiced by most, is sequences with iteration and feedback.
Most understand the idea of feedback as a control device (for those that want to brush up, a good read is Donella Meadows' book "Thinking in Systems"). So, when you combine a control device with the opportunity to do over or correct, you've got a sequence under control, and a sequence that is responsive to outcome demand.
Now, the agilists call an iterative sequence under control just common sense, or complex adaptive (perhaps so, in some cases) or emergent (closer to what actually happens). But, usually the discussion on this topic is all about the vision, the requirements backlog, and the intended product or process outcome. The risk register--indeed, the whole RM process--is often ignored, or just not in the discussion.
Where does the classic RM sequence fit in? Recall the sequence: set the context; identify risks; qualitatively and quantitatively assess the risks; plan responses; do, monitor, and control the response and its impact.
Now, how does the risk sequence fit into an agile emergent paradigm, or a iterative sequential baseline process?
I posit that the right strategy is to distribute the sequence: the first two steps, set the context and identify the risks, and be done as part of the project business case and the original envisioning. The latter steps can be allocated to the execution teams. As such, every time the backlog is reevaluated, so also is the risk register reevaluated (thus, iteration to the project charter) and the assessment, response planning, and monitor/control are incorporated into the team work of each time box or other scope segment.
So, in effect, the sequential process, with feedback, is made iterative by time box or scope segment as matter of methodology design and management policy.