Would it not be preferable to have access to the badge progress on the Badges page?
At least at those where it makes sense to show their progress (like the ones shown on the review page:
#Votes). For me it would be more intuitive to find it there. There exist already several progress indicators on badges (I do not want to provide an incomplete list of them as others can do this much better): Badge progress reports
I know that there are a badges where it makes sense and others for which it does not make sense to show their progress.