Requiring permission to do work is the enemy of progress and engineering dignity. It creates a presumption of incompetence and an atmosphere of low trust that punishes people who want to push the envelope of what's possible.
Google's design document culture is bad. Google has succeeded in spite of it.
In my experience, having worked at many large tech companies, design documents obfuscate, not enlighten. They become increasingly out-of-date as the code evolves, creating anti-documentation that makes it take longer to understand code. Yes, yes, people should update design documents as the code evolves. Everyone knows that in practice, nobody updates old design documents.
Design documents make it too easy for other developers to shoot down ideas. Sometimes the worth of code isn't apparent until it's made. It's far too easy for someone to comment "this will never work" on a proposed change. It's much harder for someone to deny benchmarks attached to a proposed change. It's too easy for reviewers to knock out functionality.
Design documents turn every feature into a half-assed, lowest-common-denominator risk-minimized barely-adequate shell of itself.
The real reason everyone at Google writes design documents is that promotion committees demand documents as "evidence of complexity". No design document, no impact. No impact, no promotion.
Code is just code. Bad changes can be backed out. It's much better to move fast and iterate quickly than to create an illusion of care and add friction to every aspect of the development process. Up-front design of software just does not work. If it did, waterfall project planning would be successful.
These questions you highlight --- Why are you making this change? What impact will it have? --- can be asked during review of actual code. There is no need to build a speedbump, not if you trust your people.
Developers should be able to choose to create design documents and solicit feedback. Most changes don't need this process. You should trust developers to know what changes require a more extensive discussion and which ones don't.
A culture that requires permissions and signoffs before work can begin is a culture that leaves products stagnant for years.