Big companies, like yours, always face a problem when it comes to maintaining their codebases. The code gets larger and larger while the velocity gets smaller and smaller. With our years of experience in consulting larger organizations, we have realized that sooner the code is properly maintained, the easier it becomes to deliver in the long run.
Most engineering managers do not focus on keeping their code-base easy to change. This becomes a developer friction and the developers start to slowly reduce their velocities. Frequent and efficient refactoring provides ways with regular sprints and development to keep this under control. We have seen many large companies get unusually big benefits in keeping their code clean and maintainable.
Efficiency of any refactoring exercise has to be identified with increases in velocity. Any other vanity metrics won't help a team to improve.
Since refactoring is mostly a technical exercise, there's no direct value addition to the customers. But instead of not understanding the value of keeping the code clean, most managers keep postponing this crucial decision. We work with managers of large companies to understand their priorities and suggest the right plans for the teams to seamlessly work on their code.