You could gamify this by generating an update score. The more often and more consistently documentation is updated relative to commits, the higher the score. Nothing will be tied to the score, it’s just a number. It’s existence would incentivize developers to drive it higher. Sure you could get around it by just adding a space to the .md file, but at least then you’re opening the file and you may see something in there that needs a quick change anyways. The score would have done its job.

This would stop working if bonuses or compensation were tied to the score. The moment that happens, people will start writing hooks to update it with a space every commit, then it will be ignored by devs.