Redesign or not depends where the business stands on processes today.
But I really do not get it that the process management community is so removed from reality. Everyone who in the slightest deals with customers learns that the one thing that customers hate is to be forced into a process that does not fit their special situation. Now the hitch is that the customer feels that his situation is ALWAYS special. And if it isn't he will make it so. Not because they are difficult on purpose but because they are HUMAN! They want to be accepted as special and not generalized. Can you imagine that you walk out of a store and say: 'I am really glad they did not make me feel special, but the classified me perfectly as being the same as 2 million other customers.' Even if they did ... you want to feel special, which is why we have sold Customer Communication Management that produces letters that read as if they were written by a person. And it goes wrong often enough because of the automated generalization.
So the one thing that you need to do to be customer-centric and to improve the customer experience is to remove ALL RIGID PROCESSES from customer interaction. It does not matter if these are IT supported or not. The illlusion is that service staff forced into a process perform better than staff that cares about the outcome. Not so, unless we talk about serving burgers at the McDonalds counter. If you have staff that does not care about the outcome that is what you need to solve and not your processes.
Yes, processes should be defined ... but through goals and outcomes and the staff must have the authority to fulfill them. That will ensure customer satisfaction. Even the most perfectly designed process flow NEVER will.