Some might even say that is because I am responsible for most of the change that I see around me. At least on projects. But that isn't fair. I recognize as well as anyone the necessity to stabilize from time to time. To slow the pace at which change is being identified and absorbed into an organization. Many of the processes and much of the effort I exert is designed specifically to assist with the absorption of change; controlling the velocity that change impacts ongoing efforts.
Don't worry about design, if you listen to your code a good design will appear...Listen to the technical people. If they are complaining about the difficulty of making changes, then take such complaints seriously and give them time to fix things.
-- Martin Fowler
Sometimes large changes are required. It is natural for individual contributors to get invested in their work and become very attached to their specific deliverables or designs. To my mind, being flexible is a critical component of competence. Without adaptability, your useful as a contributor is minimized and in some cases suspect.
Going beyond the ability to handle change as someone customer-facing is the capability to influence both the speed at which change is introduced to the delivery organization and the expectations of the customers creating that change.
To be a good lead, protect the pace of change you expect from your people. To be a good consultant, manage expectations with your clients about the changes they want to introduce.