I think that complexity is hard to measure and therefore easy to game.
At GitLab we only measure tasks completed, the number of changes that shipped to production, with the requirement that every change has to add value. This measure has been used throughout R&D https://about.gitlab.com/handbook/engineering/performance-in... to assess productivity for multiple years now with good success https://about.gitlab.com/blog/2020/08/27/measuring-engineeri...
When you tell new engineers about this target they see a great opportunity to game it, just ship smaller changes. It turns out that smaller changes are quicker to ship. Lead to better code and tests. Have lower risk of cancellation and problems in production. And lead to earlier and better feedback.
Inspired by Goodhart’s Law I'll propose the following: A measure that when it becomes a target improves productivity. ~Sijbrandij's Law