In my experience, it’s totally unnecessary to cover leather strops entirely with buffing compound. Here’s a direct link to the section of my recent sharpening guide that describes it: https://oneandawl.org/t/kemitchells-sharpening-for-new-shoemakers/166#p-698-preparation-12
With repeated coatings and recoatings, my strop surface does become more thoroughly green, though also streaked with black swarf. That might look more pleasingly uniform, but I see it more as a bad sign that I’m near the point where the wax compound has caked up enough that I’ll need to scrape it off and start again.
As long as when you drag your knife along the strop, the edge is rubbing over compound, it does the job.