The only problems are when your boss doesn't pay attention and recognize the step up, or when they actively ignore it because you've taken some of the stress of their job and they are averse to potential change/risk if they promote you.
Then you take the fact that you're outperforming your title to another company that will recognize it.
Job-hopping (done within reason) is entirely underrated. Your salary will rise at a dramatically faster rate than if you stuck around one place, your responsibilities too, and best of all you get to learn how things are done across the industry.
Not at Google, but this is how I've always treated my career. Kind of a step beyond "dress for the job you want."